diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index 649629714c3b1..1f5ba610cdeb7 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -761,6 +761,7 @@ 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/dtypes/common.py b/pandas/core/dtypes/common.py
index b8cbb41501dd1..f6e7e87f1043b 100644
--- a/pandas/core/dtypes/common.py
+++ b/pandas/core/dtypes/common.py
@@ -90,6 +90,33 @@ def ensure_categorical(arr):
     return arr
 
 
+def ensure_int64_or_float64(arr, copy=False):
+    """
+    Ensure that an dtype array of some integer dtype
+    has an int64 dtype if possible
+    If it's not possible, potentially because of overflow,
+    convert the array to float64 instead.
+
+    Parameters
+    ----------
+    arr : array-like
+          The array whose data type we want to enforce.
+    copy: boolean
+          Whether to copy the original array or reuse
+          it in place, if possible.
+
+    Returns
+    -------
+    out_arr : The input array cast as int64 if
+              possible without overflow.
+              Otherwise the input array cast to float64.
+    """
+    try:
+        return arr.astype('int64', copy=copy, casting='safe')
+    except TypeError:
+        return arr.astype('float64', copy=copy)
+
+
 def is_object_dtype(arr_or_dtype):
     """
     Check whether an array-like or dtype is of the object dtype.
diff --git a/pandas/core/groupby/ops.py b/pandas/core/groupby/ops.py
index ba04ff3a3d3ee..d9f7b4d9c31c3 100644
--- a/pandas/core/groupby/ops.py
+++ b/pandas/core/groupby/ops.py
@@ -23,6 +23,7 @@
     ensure_float64,
     ensure_platform_int,
     ensure_int64,
+    ensure_int64_or_float64,
     ensure_object,
     needs_i8_conversion,
     is_integer_dtype,
@@ -471,7 +472,7 @@ 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)
+                values = ensure_int64_or_float64(values)
         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 f8a0f1688c64e..775747ce0c6c1 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