diff --git a/cpp/src/arrow/compute/kernels/vector_sort.cc b/cpp/src/arrow/compute/kernels/vector_sort.cc
index 6c425d65550..7fa43e715d8 100644
--- a/cpp/src/arrow/compute/kernels/vector_sort.cc
+++ b/cpp/src/arrow/compute/kernels/vector_sort.cc
@@ -29,6 +29,8 @@
 #include "arrow/table.h"
 #include "arrow/type_traits.h"
 #include "arrow/util/bit_block_counter.h"
+#include "arrow/util/bitmap.h"
+#include "arrow/util/bitmap_ops.h"
 #include "arrow/util/checked_cast.h"
 #include "arrow/util/optional.h"
 #include "arrow/visitor_inline.h"
@@ -42,6 +44,7 @@ namespace internal {
 
 // Visit all physical types for which sorting is implemented.
 #define VISIT_PHYSICAL_TYPES(VISIT) \
+  VISIT(BooleanType)                \
   VISIT(Int8Type)                   \
   VISIT(Int16Type)                  \
   VISIT(Int32Type)                  \
@@ -370,6 +373,24 @@ inline void VisitRawValuesInline(const ArrayType& values,
       [&](int64_t i) { visitor_not_null(data[i]); }, [&]() { visitor_null(); });
 }
 
+template <typename VisitorNotNull, typename VisitorNull>
+inline void VisitRawValuesInline(const BooleanArray& values,
+                                 VisitorNotNull&& visitor_not_null,
+                                 VisitorNull&& visitor_null) {
+  if (values.null_count() != 0) {
+    const uint8_t* data = values.data()->GetValues<uint8_t>(1, 0);
+    VisitBitBlocksVoid(
+        values.null_bitmap(), values.offset(), values.length(),
+        [&](int64_t i) { visitor_not_null(BitUtil::GetBit(data, values.offset() + i)); },
+        [&]() { visitor_null(); });
+  } else {
+    // Can avoid GetBit() overhead in the no-nulls case
+    VisitBitBlocksVoid(
+        values.data()->buffers[1], values.offset(), values.length(),
+        [&](int64_t i) { visitor_not_null(true); }, [&]() { visitor_not_null(false); });
+  }
+}
+
 template <typename ArrowType>
 class ArrayCompareSorter {
   using ArrayType = typename TypeTraits<ArrowType>::ArrayType;
@@ -477,6 +498,42 @@ class ArrayCountSorter {
   }
 };
 
+using ::arrow::internal::Bitmap;
+
+template <>
+class ArrayCountSorter<BooleanType> {
+ public:
+  ArrayCountSorter() = default;
+
+  // Returns where null starts.
+  // `offset` is used when this is called on a chunk of a chunked array
+  uint64_t* Sort(uint64_t* indices_begin, uint64_t* indices_end,
+                 const BooleanArray& values, int64_t offset,
+                 const ArraySortOptions& options) {
+    std::array<int64_t, 2> counts{0, 0};
+
+    const int64_t nulls = values.null_count();
+    const int64_t ones = values.true_count();
+    const int64_t zeros = values.length() - ones - nulls;
+
+    int64_t null_position = values.length() - nulls;
+    int64_t index = offset;
+    const auto nulls_begin = indices_begin + null_position;
+
+    if (options.order == SortOrder::Ascending) {
+      // ones start after zeros
+      counts[1] = zeros;
+    } else {
+      // zeros start after ones
+      counts[0] = ones;
+    }
+    VisitRawValuesInline(
+        values, [&](bool v) { indices_begin[counts[v]++] = index++; },
+        [&]() { indices_begin[null_position++] = index++; });
+    return nulls_begin;
+  }
+};
+
 // Sort integers with counting sort or comparison based sorting algorithm
 // - Use O(n) counting sort if values are in a small range
 // - Use O(nlogn) std::stable_sort otherwise
@@ -527,6 +584,11 @@ class ArrayCountOrCompareSorter {
 template <typename Type, typename Enable = void>
 struct ArraySorter;
 
+template <>
+struct ArraySorter<BooleanType> {
+  ArrayCountSorter<BooleanType> impl;
+};
+
 template <>
 struct ArraySorter<UInt8Type> {
   ArrayCountSorter<UInt8Type> impl;
@@ -576,11 +638,17 @@ struct ArraySortIndices {
 
 // Sort indices kernels implemented for
 //
+// * Boolean type
 // * Number types
 // * Base binary types
 
 template <template <typename...> class ExecTemplate>
 void AddSortingKernels(VectorKernel base, VectorFunction* func) {
+  // bool type
+  base.signature = KernelSignature::Make({InputType::Array(boolean())}, uint64());
+  base.exec = ExecTemplate<UInt64Type, BooleanType>::Exec;
+  DCHECK_OK(func->AddKernel(base));
+
   for (const auto& ty : NumericTypes()) {
     auto physical_type = GetPhysicalType(ty);
     base.signature = KernelSignature::Make({InputType::Array(ty)}, uint64());
diff --git a/cpp/src/arrow/compute/kernels/vector_sort_benchmark.cc b/cpp/src/arrow/compute/kernels/vector_sort_benchmark.cc
index 820c51ba8ec..d8e3b9b8081 100644
--- a/cpp/src/arrow/compute/kernels/vector_sort_benchmark.cc
+++ b/cpp/src/arrow/compute/kernels/vector_sort_benchmark.cc
@@ -81,6 +81,16 @@ static void ArraySortIndicesInt64Wide(benchmark::State& state) {
   ArraySortIndicesInt64Benchmark(state, min, max);
 }
 
+static void ArraySortIndicesBool(benchmark::State& state) {
+  RegressionArgs args(state);
+
+  const int64_t array_size = args.size * 8;
+  auto rand = random::RandomArrayGenerator(kSeed);
+  auto values = rand.Boolean(array_size, 0.5, args.null_proportion);
+
+  ArraySortIndicesBenchmark(state, values);
+}
+
 static void ChunkedArraySortIndicesInt64Narrow(benchmark::State& state) {
   ChunkedArraySortIndicesInt64Benchmark(state, -100, 100);
 }
@@ -235,6 +245,12 @@ BENCHMARK(ArraySortIndicesInt64Wide)
     ->Args({1 << 23, 100})
     ->Unit(benchmark::TimeUnit::kNanosecond);
 
+BENCHMARK(ArraySortIndicesBool)
+    ->Apply(RegressionSetArgs)
+    ->Args({1 << 20, 100})
+    ->Args({1 << 23, 100})
+    ->Unit(benchmark::TimeUnit::kNanosecond);
+
 BENCHMARK(ChunkedArraySortIndicesInt64Narrow)
     ->Apply(RegressionSetArgs)
     ->Args({1 << 20, 100})
diff --git a/cpp/src/arrow/compute/kernels/vector_sort_test.cc b/cpp/src/arrow/compute/kernels/vector_sort_test.cc
index 2d76f0102f0..478f6ccac3a 100644
--- a/cpp/src/arrow/compute/kernels/vector_sort_test.cc
+++ b/cpp/src/arrow/compute/kernels/vector_sort_test.cc
@@ -180,6 +180,10 @@ template <typename ArrowType>
 class TestNthToIndicesForIntegral : public TestNthToIndices<ArrowType> {};
 TYPED_TEST_SUITE(TestNthToIndicesForIntegral, IntegralArrowTypes);
 
+template <typename ArrowType>
+class TestNthToIndicesForBool : public TestNthToIndices<ArrowType> {};
+TYPED_TEST_SUITE(TestNthToIndicesForBool, ::testing::Types<BooleanType>);
+
 template <typename ArrowType>
 class TestNthToIndicesForTemporal : public TestNthToIndices<ArrowType> {};
 TYPED_TEST_SUITE(TestNthToIndicesForTemporal, TemporalArrowTypes);
@@ -223,6 +227,13 @@ TYPED_TEST(TestNthToIndicesForIntegral, Integral) {
   this->AssertNthToIndicesJson("[null, 1, 3, null, 2, 5]", 6);
 }
 
+TYPED_TEST(TestNthToIndicesForBool, Bool) {
+  this->AssertNthToIndicesJson("[null, false, true, null, false, true]", 0);
+  this->AssertNthToIndicesJson("[null, false, true, null, false, true]", 2);
+  this->AssertNthToIndicesJson("[null, false, true, null, false, true]", 5);
+  this->AssertNthToIndicesJson("[null, false, true, null, false, true]", 6);
+}
+
 TYPED_TEST(TestNthToIndicesForTemporal, Temporal) {
   this->AssertNthToIndicesJson("[null, 1, 3, null, 2, 5]", 0);
   this->AssertNthToIndicesJson("[null, 1, 3, null, 2, 5]", 2);
@@ -402,6 +413,10 @@ template <typename ArrowType>
 class TestArraySortIndicesForReal : public TestArraySortIndices<ArrowType> {};
 TYPED_TEST_SUITE(TestArraySortIndicesForReal, RealArrowTypes);
 
+template <typename ArrowType>
+class TestArraySortIndicesForBool : public TestArraySortIndices<ArrowType> {};
+TYPED_TEST_SUITE(TestArraySortIndicesForBool, ::testing::Types<BooleanType>);
+
 template <typename ArrowType>
 class TestArraySortIndicesForIntegral : public TestArraySortIndices<ArrowType> {};
 TYPED_TEST_SUITE(TestArraySortIndicesForIntegral, IntegralArrowTypes);
@@ -464,6 +479,26 @@ TYPED_TEST(TestArraySortIndicesForIntegral, SortIntegral) {
                           "[5, 2, 4, 1, 0, 3]");
 }
 
+TYPED_TEST(TestArraySortIndicesForBool, SortBool) {
+  this->AssertSortIndices("[]", "[]");
+
+  this->AssertSortIndices("[true, true, false]", "[2, 0, 1]");
+  this->AssertSortIndices("[false, false,  false, true, true, true, true]",
+                          "[0, 1, 2, 3, 4, 5, 6]");
+  this->AssertSortIndices("[true, true, true, true, false, false, false]",
+                          "[4, 5, 6, 0, 1, 2, 3]");
+
+  this->AssertSortIndices("[false, true, false, true, true, false, false]",
+                          SortOrder::Ascending, "[0, 2, 5, 6, 1, 3, 4]");
+  this->AssertSortIndices("[false, true, false, true, true, false, false]",
+                          SortOrder::Descending, "[1, 3, 4, 0, 2, 5, 6]");
+
+  this->AssertSortIndices("[null, true, false, null, false, true]", SortOrder::Ascending,
+                          "[2, 4, 1, 5, 0, 3]");
+  this->AssertSortIndices("[null, true, false, null, false, true]", SortOrder::Descending,
+                          "[1, 5, 2, 4, 0, 3]");
+}
+
 TYPED_TEST(TestArraySortIndicesForTemporal, SortTemporal) {
   this->AssertSortIndices("[]", "[]");
 
@@ -546,7 +581,7 @@ class TestArraySortIndicesRandomCompare : public TestBase {};
 using SortIndicesableTypes =
     ::testing::Types<UInt8Type, UInt16Type, UInt32Type, UInt64Type, Int8Type, Int16Type,
                      Int32Type, Int64Type, FloatType, DoubleType, StringType,
-                     Decimal128Type>;
+                     Decimal128Type, BooleanType>;
 
 template <typename ArrayType>
 void ValidateSorted(const ArrayType& array, UInt64Array& offsets, SortOrder order) {
@@ -842,6 +877,27 @@ TEST_F(TestRecordBatchSortIndices, NaNAndNull) {
   AssertSortIndices(batch, options, "[7, 1, 2, 6, 5, 4, 0, 3]");
 }
 
+TEST_F(TestRecordBatchSortIndices, Boolean) {
+  auto schema = ::arrow::schema({
+      {field("a", boolean())},
+      {field("b", boolean())},
+  });
+  SortOptions options(
+      {SortKey("a", SortOrder::Ascending), SortKey("b", SortOrder::Descending)});
+
+  auto batch = RecordBatchFromJSON(schema,
+                                   R"([{"a": true,    "b": null},
+                                       {"a": false,   "b": null},
+                                       {"a": true,    "b": true},
+                                       {"a": false,   "b": true},
+                                       {"a": true,    "b": false},
+                                       {"a": null,    "b": false},
+                                       {"a": false,   "b": null},
+                                       {"a": null,    "b": true}
+                                       ])");
+  AssertSortIndices(batch, options, "[3, 1, 6, 2, 4, 0, 7, 5]");
+}
+
 TEST_F(TestRecordBatchSortIndices, MoreTypes) {
   auto schema = ::arrow::schema({
       {field("a", timestamp(TimeUnit::MICRO))},
@@ -980,6 +1036,25 @@ TEST_F(TestTableSortIndices, NaNAndNull) {
   AssertSortIndices(table, options, "[7, 1, 2, 6, 5, 4, 0, 3]");
 }
 
+TEST_F(TestTableSortIndices, Boolean) {
+  auto schema = ::arrow::schema({
+      {field("a", boolean())},
+      {field("b", boolean())},
+  });
+  SortOptions options(
+      {SortKey("a", SortOrder::Ascending), SortKey("b", SortOrder::Descending)});
+  auto table = TableFromJSON(schema, {R"([{"a": true,    "b": null},
+                                       {"a": false,   "b": null},
+                                       {"a": true,    "b": true},
+                                       {"a": false,   "b": true}])",
+                                      R"([{"a": true,    "b": false},
+                                       {"a": null,    "b": false},
+                                       {"a": false,   "b": null},
+                                       {"a": null,    "b": true}
+                                       ])"});
+  AssertSortIndices(table, options, "[3, 1, 6, 2, 4, 0, 7, 5]");
+}
+
 TEST_F(TestTableSortIndices, BinaryLike) {
   auto schema = ::arrow::schema({
       {field("a", large_utf8())},
diff --git a/docs/source/cpp/compute.rst b/docs/source/cpp/compute.rst
index 4bcb568fdc2..b389b43c02e 100644
--- a/docs/source/cpp/compute.rst
+++ b/docs/source/cpp/compute.rst
@@ -1163,21 +1163,21 @@ In these functions, nulls are considered greater than any other value
 Floating-point NaN values are considered greater than any other non-null
 value, but smaller than nulls.
 
-+-----------------------+------------+-------------------------+-------------------+--------------------------------+----------------+
-| Function name         | Arity      | Input types             | Output type       | Options class                  | Notes          |
-+=======================+============+=========================+===================+================================+================+
-| partition_nth_indices | Unary      | Binary- and String-like | UInt64            | :struct:`PartitionNthOptions`  | \(1) \(3)      |
-+-----------------------+------------+-------------------------+-------------------+--------------------------------+----------------+
-| partition_nth_indices | Unary      | Numeric                 | UInt64            | :struct:`PartitionNthOptions`  | \(1)           |
-+-----------------------+------------+-------------------------+-------------------+--------------------------------+----------------+
-| array_sort_indices    | Unary      | Binary- and String-like | UInt64            | :struct:`ArraySortOptions`     | \(2) \(3) \(4) |
-+-----------------------+------------+-------------------------+-------------------+--------------------------------+----------------+
-| array_sort_indices    | Unary      | Numeric                 | UInt64            | :struct:`ArraySortOptions`     | \(2) \(4)      |
-+-----------------------+------------+-------------------------+-------------------+--------------------------------+----------------+
-| sort_indices          | Unary      | Binary- and String-like | UInt64            | :struct:`SortOptions`          | \(2) \(3) \(5) |
-+-----------------------+------------+-------------------------+-------------------+--------------------------------+----------------+
-| sort_indices          | Unary      | Numeric                 | UInt64            | :struct:`SortOptions`          | \(2) \(5)      |
-+-----------------------+------------+-------------------------+-------------------+--------------------------------+----------------+
++-----------------------+------------+-----------------------------+-------------------+--------------------------------+----------------+
+| Function name         | Arity      | Input types                 | Output type       | Options class                  | Notes          |
++=======================+============+=============================+===================+================================+================+
+| partition_nth_indices | Unary      | Binary- and String-like     | UInt64            | :struct:`PartitionNthOptions`  | \(1) \(3)      |
++-----------------------+------------+-----------------------------+-------------------+--------------------------------+----------------+
+| partition_nth_indices | Unary      | Boolean, Numeric, Temporal  | UInt64            | :struct:`PartitionNthOptions`  | \(1)           |
++-----------------------+------------+-----------------------------+-------------------+--------------------------------+----------------+
+| array_sort_indices    | Unary      | Binary- and String-like     | UInt64            | :struct:`ArraySortOptions`     | \(2) \(3) \(4) |
++-----------------------+------------+-----------------------------+-------------------+--------------------------------+----------------+
+| array_sort_indices    | Unary      | Boolean, Numeric, Temporal  | UInt64            | :struct:`ArraySortOptions`     | \(2) \(4)      |
++-----------------------+------------+-----------------------------+-------------------+--------------------------------+----------------+
+| sort_indices          | Unary      | Binary- and String-like     | UInt64            | :struct:`SortOptions`          | \(2) \(3) \(5) |
++-----------------------+------------+-----------------------------+-------------------+--------------------------------+----------------+
+| sort_indices          | Unary      | Boolean, Numeric, Temporal  | UInt64            | :struct:`SortOptions`          | \(2) \(5)      |
++-----------------------+------------+-----------------------------+-------------------+--------------------------------+----------------+
 
 * \(1) The output is an array of indices into the input array, that define
   a partial non-stable sort such that the *N*'th index points to the *N*'th
diff --git a/r/tests/testthat/helper-data.R b/r/tests/testthat/helper-data.R
index 43b5bf0354f..b4b1bac4d7b 100644
--- a/r/tests/testthat/helper-data.R
+++ b/r/tests/testthat/helper-data.R
@@ -152,7 +152,7 @@ example_data_for_sorting <- tibble::tibble(
   int = c(-.Machine$integer.max, -101L, -100L, 0L, 0L, 1L, 100L, 1000L, .Machine$integer.max, NA_integer_),
   dbl = c(-Inf, -.Machine$double.xmax, -.Machine$double.xmin, 0, .Machine$double.xmin, pi, .Machine$double.xmax, Inf, NaN, NA_real_),
   chr = c("", "", "\"", "&", "ABC", "NULL", "a", "abc", "zzz", NA_character_),
-  lgl = c(rep(FALSE, 4L), rep(TRUE, 5L), NA), # bool is not supported (ARROW-12016)
+  lgl = c(rep(FALSE, 4L), rep(TRUE, 5L), NA),
   dttm = lubridate::ymd_hms(c(
     "0000-01-01 00:00:00",
     "1919-05-29 13:08:55",
diff --git a/r/tests/testthat/test-dplyr-arrange.R b/r/tests/testthat/test-dplyr-arrange.R
index 6e663d23ec6..5131653146b 100644
--- a/r/tests/testthat/test-dplyr-arrange.R
+++ b/r/tests/testthat/test-dplyr-arrange.R
@@ -159,7 +159,6 @@ test_that("arrange() on datetime columns", {
 })
 
 test_that("arrange() on logical columns", {
-  skip("Sorting by bool columns is not supported (ARROW-12016)")
   expect_dplyr_equal(
     input %>%
       arrange(lgl, int) %>%