diff --git a/doc/recipe/preprocessor.rst b/doc/recipe/preprocessor.rst
index 6b372b9143..fecf8f7007 100644
--- a/doc/recipe/preprocessor.rst
+++ b/doc/recipe/preprocessor.rst
@@ -926,10 +926,23 @@ example of its usage in an ESMValTool preprocessor is:
             reference: esmf_regrid.schemes:ESMFAreaWeighted
             mdtol: 0.7
 
-.. TODO: Remove the following warning once things have settled a bit.
-.. warning::
-   Just as the mesh support in Iris itself, this new regridding package is
-   still considered experimental.
+Additionally, the use of generic schemes that take source and target grid cubes as
+arguments is also supported. The call function for such schemes must be defined as
+`(src_cube, grid_cube, **kwargs)` and they must return `iris.cube.Cube` objects.
+The `regrid` module will automatically pass the source and grid cubes as inputs
+of the scheme. An example of this usage is
+the :func:`~esmf_regrid.schemes.regrid_rectilinear_to_rectilinear`
+scheme available in :doc:`iris-esmf-regrid:index`:git 
+
+.. code-block:: yaml
+
+    preprocessors:
+      regrid_preprocessor:
+        regrid:
+          target_grid: 2.5x2.5
+          scheme:
+            reference: esmf_regrid.schemes:regrid_rectilinear_to_rectilinear
+            mdtol: 0.7
 
 .. _ensemble statistics:
 
diff --git a/environment.yml b/environment.yml
index d155273c23..43e16206ea 100644
--- a/environment.yml
+++ b/environment.yml
@@ -18,6 +18,7 @@ dependencies:
   - humanfriendly
   - importlib_resources
   - iris>=3.2.1
+  - iris-esmf-regrid
   - isodate
   - jinja2
   - nc-time-axis
diff --git a/esmvalcore/preprocessor/_regrid.py b/esmvalcore/preprocessor/_regrid.py
index ea505fbbdf..eabbfd853e 100644
--- a/esmvalcore/preprocessor/_regrid.py
+++ b/esmvalcore/preprocessor/_regrid.py
@@ -1,6 +1,7 @@
 """Horizontal and vertical regridding module."""
 
 import importlib
+import inspect
 import logging
 import os
 import re
@@ -536,8 +537,7 @@ def regrid(cube, target_grid, scheme, lat_offset=True, lon_offset=True):
               extrapolation_mode: nanmask
 
     To use the area weighted regridder available in
-    :class:`esmf_regrid.schemes.ESMFAreaWeighted`, make sure that
-    :doc:`iris-esmf-regrid:index` is installed and use
+    :class:`esmf_regrid.schemes.ESMFAreaWeighted` use
 
     .. code-block:: yaml
 
@@ -547,34 +547,7 @@ def regrid(cube, target_grid, scheme, lat_offset=True, lon_offset=True):
             scheme:
               reference: esmf_regrid.schemes:ESMFAreaWeighted
 
-    .. note::
-
-        Note that :doc:`iris-esmf-regrid:index` is still experimental.
     """
-    if isinstance(scheme, dict):
-        try:
-            object_ref = scheme.pop("reference")
-        except KeyError as key_err:
-            raise ValueError(
-                "No reference specified for generic regridding.") from key_err
-        module_name, separator, scheme_name = object_ref.partition(":")
-        try:
-            obj = importlib.import_module(module_name)
-        except ImportError as import_err:
-            raise ValueError(
-                "Could not import specified generic regridding module. "
-                "Please double check spelling and that the required module is "
-                "installed.") from import_err
-        if separator:
-            for attr in scheme_name.split('.'):
-                obj = getattr(obj, attr)
-        loaded_scheme = obj(**scheme)
-    else:
-        loaded_scheme = HORIZONTAL_SCHEMES.get(scheme.lower())
-    if loaded_scheme is None:
-        emsg = 'Unknown regridding scheme, got {!r}.'
-        raise ValueError(emsg.format(scheme))
-
     if isinstance(target_grid, str):
         if os.path.isfile(target_grid):
             target_grid = iris.load_cube(target_grid)
@@ -592,7 +565,6 @@ def regrid(cube, target_grid, scheme, lat_offset=True, lon_offset=True):
             ycoord = target_grid.coord(axis='y', dim_coords=True)
             xcoord.coord_system = src_cs
             ycoord.coord_system = src_cs
-
     elif isinstance(target_grid, dict):
         # Generate a target grid from the provided specification,
         target_grid = _regional_stock_cube(target_grid)
@@ -600,6 +572,39 @@ def regrid(cube, target_grid, scheme, lat_offset=True, lon_offset=True):
     if not isinstance(target_grid, iris.cube.Cube):
         raise ValueError(f'Expecting a cube, got {target_grid}.')
 
+    if isinstance(scheme, dict):
+        try:
+            object_ref = scheme.pop("reference")
+        except KeyError as key_err:
+            raise ValueError(
+                "No reference specified for generic regridding.") from key_err
+        module_name, separator, scheme_name = object_ref.partition(":")
+        try:
+            obj = importlib.import_module(module_name)
+        except ImportError as import_err:
+            raise ValueError(
+                "Could not import specified generic regridding module. "
+                "Please double check spelling and that the required module is "
+                "installed.") from import_err
+        if separator:
+            for attr in scheme_name.split('.'):
+                obj = getattr(obj, attr)
+
+        scheme_args = inspect.getfullargspec(obj).args
+        # Add source and target cubes as arguments if required
+        if 'src_cube' in scheme_args:
+            scheme['src_cube'] = cube
+        if 'grid_cube' in scheme_args:
+            scheme['grid_cube'] = target_grid
+
+        loaded_scheme = obj(**scheme)
+    else:
+        loaded_scheme = HORIZONTAL_SCHEMES.get(scheme.lower())
+
+    if loaded_scheme is None:
+        emsg = 'Unknown regridding scheme, got {!r}.'
+        raise ValueError(emsg.format(scheme))
+
     # Unstructured regridding requires x2 2d spatial coordinates,
     # so ensure to purge any 1d native spatial dimension coordinates
     # for the regridder.
@@ -629,6 +634,10 @@ def regrid(cube, target_grid, scheme, lat_offset=True, lon_offset=True):
         # Perform the horizontal regridding
         if _attempt_irregular_regridding(cube, scheme):
             cube = esmpy_regrid(cube, target_grid, scheme)
+        elif isinstance(loaded_scheme, iris.cube.Cube):
+            # Return regridded cube in cases in which the
+            # scheme is a function f(src_cube, grid_cube) -> Cube
+            return loaded_scheme
         else:
             cube = cube.regrid(target_grid, loaded_scheme)
 
diff --git a/setup.py b/setup.py
index 514c41e744..3a732d09c3 100755
--- a/setup.py
+++ b/setup.py
@@ -32,6 +32,7 @@
         'cf-units',
         'dask[array]',
         'esgf-pyclient>=0.3.1',
+        'esmf-regrid',
         'esmpy!=8.1.0',  # see github.com/ESMValGroup/ESMValCore/issues/1208
         'fiona',
         'fire',
diff --git a/tests/integration/preprocessor/_regrid/test_regrid.py b/tests/integration/preprocessor/_regrid/test_regrid.py
index a6ba8b95b5..8a720d461f 100644
--- a/tests/integration/preprocessor/_regrid/test_regrid.py
+++ b/tests/integration/preprocessor/_regrid/test_regrid.py
@@ -92,6 +92,18 @@ def test_regrid__linear(self):
         expected = np.array([[[1.5]], [[5.5]], [[9.5]]])
         self.assert_array_equal(result.data, expected)
 
+    def test_regrid__esmf_rectilinear(self):
+        scheme_name = 'esmf_regrid.schemes:regrid_rectilinear_to_rectilinear'
+        scheme = {
+            'reference': scheme_name
+        }
+        result = regrid(
+            self.cube,
+            self.grid_for_linear,
+            scheme)
+        expected = np.array([[[1.5]], [[5.5]], [[9.5]]])
+        np.testing.assert_array_almost_equal(result.data, expected, decimal=1)
+
     def test_regrid__regular_coordinates(self):
         data = np.ones((1, 1))
         lons = iris.coords.DimCoord([1.50000000000001],
@@ -214,6 +226,27 @@ def test_regrid__area_weighted(self):
         expected = np.array([1.499886, 5.499886, 9.499886])
         np.testing.assert_array_almost_equal(result.data, expected, decimal=6)
 
+    def test_regrid__esmf_area_weighted(self):
+        data = np.empty((1, 1))
+        lons = iris.coords.DimCoord([1.6],
+                                    standard_name='longitude',
+                                    bounds=[[1, 2]],
+                                    units='degrees_east',
+                                    coord_system=self.cs)
+        lats = iris.coords.DimCoord([1.6],
+                                    standard_name='latitude',
+                                    bounds=[[1, 2]],
+                                    units='degrees_north',
+                                    coord_system=self.cs)
+        coords_spec = [(lats, 0), (lons, 1)]
+        grid = iris.cube.Cube(data, dim_coords_and_dims=coords_spec)
+        scheme = {
+            'reference': 'esmf_regrid.schemes:ESMFAreaWeighted'
+        }
+        result = regrid(self.cube, grid, scheme)
+        expected = np.array([[[1.499886]], [[5.499886]], [[9.499886]]])
+        np.testing.assert_array_almost_equal(result.data, expected, decimal=6)
+
     def test_regrid__unstructured_nearest_float(self):
         """Test unstructured_nearest regridding with cube of floats."""
         result = regrid(self.unstructured_grid_cube,
diff --git a/tests/unit/preprocessor/_regrid/test_regrid.py b/tests/unit/preprocessor/_regrid/test_regrid.py
index 3846ccac81..06001589b1 100644
--- a/tests/unit/preprocessor/_regrid/test_regrid.py
+++ b/tests/unit/preprocessor/_regrid/test_regrid.py
@@ -103,10 +103,9 @@ def test_invalid_tgt_grid__unknown(self):
             regrid(self.src_cube, dummy, scheme)
 
     def test_invalid_scheme__unknown(self):
-        dummy = mock.sentinel.dummy
         emsg = 'Unknown regridding scheme'
         with self.assertRaisesRegex(ValueError, emsg):
-            regrid(dummy, dummy, 'wibble')
+            regrid(self.src_cube, self.src_cube, 'wibble')
 
     def test_horizontal_schemes(self):
         self.assertEqual(