diff --git a/dvc/output/local.py b/dvc/output/local.py
index 0e1b72dc97..6e4123d1e3 100644
--- a/dvc/output/local.py
+++ b/dvc/output/local.py
@@ -18,6 +18,12 @@ class OutputLOCAL(OutputBase):
     REMOTE = RemoteLOCAL
     sep = os.sep
 
+    def __init__(self, stage, path, *args, **kwargs):
+        if stage and path_isin(path, stage.repo.root_dir):
+            path = relpath(path, stage.wdir)
+
+        super().__init__(stage, path, *args, **kwargs)
+
     def _parse_path(self, remote, path):
         parsed = urlparse(path)
         if parsed.scheme == "remote":
diff --git a/tests/func/test_add.py b/tests/func/test_add.py
index 1ce44a0b0b..002722f52b 100644
--- a/tests/func/test_add.py
+++ b/tests/func/test_add.py
@@ -216,7 +216,7 @@ def test(self):
         self.assertEqual(ret, 0)
 
         d = load_stage_file("bar.dvc")
-        self.assertEqual(d["outs"][0]["path"], bar)
+        self.assertEqual(d["outs"][0]["path"], self.BAR)
 
 
 class TestCmdAdd(TestDvc):
diff --git a/tests/unit/output/test_local.py b/tests/unit/output/test_local.py
index 50059e6eae..ef029d2940 100644
--- a/tests/unit/output/test_local.py
+++ b/tests/unit/output/test_local.py
@@ -42,13 +42,28 @@ def test_str_workdir_inside_repo(dvc):
     assert os.path.join("some_folder", "path") == str(output)
 
 
-def test_str_on_absolute_path(dvc):
+def test_str_on_local_absolute_path(dvc):
     stage = Stage(dvc)
 
-    path = os.path.abspath(os.path.join("path", "to", "file"))
-    output = OutputLOCAL(stage, path, cache=False)
+    rel_path = os.path.join("path", "to", "file")
+    abs_path = os.path.abspath(rel_path)
+    output = OutputLOCAL(stage, abs_path, cache=False)
 
-    assert path == str(output)
+    assert output.def_path == rel_path
+    assert output.path_info.fspath == abs_path
+    assert str(output) == rel_path
+
+
+def test_str_on_external_absolute_path(dvc):
+    stage = Stage(dvc)
+
+    rel_path = os.path.join("..", "path", "to", "file")
+    abs_path = os.path.abspath(rel_path)
+    output = OutputLOCAL(stage, abs_path, cache=False)
+
+    assert output.def_path == abs_path
+    assert output.path_info.fspath == abs_path
+    assert str(output) == abs_path
 
 
 class TestGetFilesNumber(TestDvc):