diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index fb7af00f615349..79595b79cddb16 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -754,6 +754,7 @@ Groupby/Resample/Rolling
 - Bug in :meth:`Resampler.apply` when passing postiional arguments to applied func (:issue:`14615`).
 - Bug in :meth:`Series.resample` when passing ``numpy.timedelta64`` to `loffset` kwarg (:issue:`7687`).
 - Bug in :meth:`Resampler.asfreq` when frequency of ``TimedeltaIndex`` is a subperiod of a new frequency (:issue:`13022`).
+- Bug in :meth:`SeriesGroupBy.mean` when values were integral but could not fit inside of int64, overflowing instead. (:issue:`22487`)
 
 Sparse
 ^^^^^^
diff --git a/pandas/core/groupby/ops.py b/pandas/core/groupby/ops.py
index ba04ff3a3d3eee..c2d000f1f44b14 100644
--- a/pandas/core/groupby/ops.py
+++ b/pandas/core/groupby/ops.py
@@ -471,7 +471,12 @@ def _cython_operation(self, kind, values, how, axis, min_count=-1,
             if (values == iNaT).any():
                 values = ensure_float64(values)
             else:
-                values = values.astype('int64', copy=False)
+                try:
+                    values = values.astype('int64', copy=False, casting='safe')
+                except TypeError:
+                    # At least one of the integers were outside the range of
+                    # int64. Convert to float64 instead.
+                    values = values.astype('float64', copy=False)
         elif is_numeric and not is_complex_dtype(values):
             values = ensure_float64(values)
         else:
diff --git a/pandas/tests/groupby/test_function.py b/pandas/tests/groupby/test_function.py
index f8a0f1688c64e0..775747ce0c6c11 100644
--- a/pandas/tests/groupby/test_function.py
+++ b/pandas/tests/groupby/test_function.py
@@ -1125,3 +1125,12 @@ def h(df, arg3):
     expected = pd.Series([4, 8, 12], index=pd.Int64Index([1, 2, 3]))
 
     tm.assert_series_equal(result, expected)
+
+
+def test_groupby_mean_no_overflow():
+    # Regression test for (#22487)
+    df = pd.DataFrame({
+        "user": ["A", "A", "A", "A", "A"],
+        "connections": [4970, 4749, 4719, 4704, 18446744073699999744]
+    })
+    assert df.groupby('user')['connections'].mean()['A'] == 3689348814740003840