diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 814dbe999d5c1..0e61d1acfb022 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -640,6 +640,43 @@ The method :meth:`core.DataFrameGroupBy.size` would previously ignore ``as_index
 
    df.groupby("a", as_index=False).size()
 
+.. _whatsnew_110.api_breaking.groupby_results_lost_as_index_false:
+
+:meth:`DataFrameGroupby.agg` lost results with ``as_index`` ``False`` when relabeling columns
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Previously :meth:`DataFrameGroupby.agg` lost the result columns, when the ``as_index`` option was
+set to ``False`` and the result columns were relabeled. In this case he result values were replaced with
+the previous index (:issue:`32240`).
+
+.. ipython:: python
+
+   df = pd.DataFrame({"key": ["x", "y", "z", "x", "y", "z"],
+                      "val": [1.0, 0.8, 2.0, 3.0, 3.6, 0.75]})
+   df
+
+*Previous behavior*:
+
+.. code-block:: ipython
+
+   In [2]: grouped = df.groupby("key", as_index=False)
+   In [3]: result = grouped.agg(min_val=pd.NamedAgg(column="val", aggfunc="min"))
+   In [4]: result
+   Out[4]:
+        min_val
+    0 	x
+    1 	y
+    2 	z
+
+*New behavior*:
+
+.. ipython:: python
+
+   grouped = df.groupby("key", as_index=False)
+   result = grouped.agg(min_val=pd.NamedAgg(column="val", aggfunc="min"))
+   result
+
+
 .. _whatsnew_110.notable_bug_fixes.apply_applymap_first_once:
 
 apply and applymap on ``DataFrame`` evaluates first row/column only once
diff --git a/pandas/core/groupby/generic.py b/pandas/core/groupby/generic.py
index b9a8f3d5a5176..1d14361757e4a 100644
--- a/pandas/core/groupby/generic.py
+++ b/pandas/core/groupby/generic.py
@@ -975,16 +975,16 @@ def aggregate(self, func=None, *args, engine=None, engine_kwargs=None, **kwargs)
                         [self._selected_obj.columns.name] * result.columns.nlevels
                     ).droplevel(-1)
 
-        if not self.as_index:
-            self._insert_inaxis_grouper_inplace(result)
-            result.index = np.arange(len(result))
-
         if relabeling:
 
             # used reordered index of columns
             result = result.iloc[:, order]
             result.columns = columns
 
+        if not self.as_index:
+            self._insert_inaxis_grouper_inplace(result)
+            result.index = np.arange(len(result))
+
         return result._convert(datetime=True)
 
     agg = aggregate
diff --git a/pandas/tests/groupby/aggregate/test_aggregate.py b/pandas/tests/groupby/aggregate/test_aggregate.py
index bf465635c0085..40a20c8210052 100644
--- a/pandas/tests/groupby/aggregate/test_aggregate.py
+++ b/pandas/tests/groupby/aggregate/test_aggregate.py
@@ -795,6 +795,41 @@ def test_groupby_aggregate_empty_key_empty_return():
     tm.assert_frame_equal(result, expected)
 
 
+def test_grouby_agg_loses_results_with_as_index_false_relabel():
+    # GH 32240: When the aggregate function relabels column names and
+    # as_index=False is specified, the results are dropped.
+
+    df = pd.DataFrame(
+        {"key": ["x", "y", "z", "x", "y", "z"], "val": [1.0, 0.8, 2.0, 3.0, 3.6, 0.75]}
+    )
+
+    grouped = df.groupby("key", as_index=False)
+    result = grouped.agg(min_val=pd.NamedAgg(column="val", aggfunc="min"))
+    expected = pd.DataFrame({"key": ["x", "y", "z"], "min_val": [1.0, 0.8, 0.75]})
+    tm.assert_frame_equal(result, expected)
+
+
+def test_grouby_agg_loses_results_with_as_index_false_relabel_multiindex():
+    # GH 32240: When the aggregate function relabels column names and
+    # as_index=False is specified, the results are dropped. Check if
+    # multiindex is returned in the right order
+
+    df = pd.DataFrame(
+        {
+            "key": ["x", "y", "x", "y", "x", "x"],
+            "key1": ["a", "b", "c", "b", "a", "c"],
+            "val": [1.0, 0.8, 2.0, 3.0, 3.6, 0.75],
+        }
+    )
+
+    grouped = df.groupby(["key", "key1"], as_index=False)
+    result = grouped.agg(min_val=pd.NamedAgg(column="val", aggfunc="min"))
+    expected = pd.DataFrame(
+        {"key": ["x", "x", "y"], "key1": ["a", "c", "b"], "min_val": [1.0, 0.75, 0.8]}
+    )
+    tm.assert_frame_equal(result, expected)
+
+
 @pytest.mark.parametrize(
     "func", [lambda s: s.mean(), lambda s: np.mean(s), lambda s: np.nanmean(s)]
 )