diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index 3c4b38a93b8ee..18ab118c4bf16 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -698,6 +698,7 @@ Deprecations
 - Deprecated passing arguments (apart from ``value``) as positional in :meth:`DataFrame.fillna` and :meth:`Series.fillna` (:issue:`41485`)
 - Deprecated passing arguments as positional in :meth:`DataFrame.reset_index` (other than ``"level"``) and :meth:`Series.reset_index` (:issue:`41485`)
 - Deprecated construction of :class:`Series` or :class:`DataFrame` with ``DatetimeTZDtype`` data and ``datetime64[ns]`` dtype.  Use ``Series(data).dt.tz_localize(None)`` instead (:issue:`41555`,:issue:`33401`)
+- Deprecated behavior of :class:`Series` construction with large-integer values and small-integer dtype silently overflowing; use ``Series(data).astype(dtype)`` instead (:issue:`41734`)
 - Deprecated inference of ``timedelta64[ns]``, ``datetime64[ns]``, or ``DatetimeTZDtype`` dtypes in :class:`Series` construction when data containing strings is passed and no ``dtype`` is passed (:issue:`33558`)
 - In a future version, constructing :class:`Series` or :class:`DataFrame` with ``datetime64[ns]`` data and ``DatetimeTZDtype`` will treat the data as wall-times instead of as UTC times (matching DatetimeIndex behavior). To treat the data as UTC times, use ``pd.Series(data).dt.tz_localize("UTC").dt.tz_convert(dtype.tz)`` or ``pd.Series(data.view("int64"), dtype=dtype)`` (:issue:`33401`)
 - Deprecated passing arguments as positional in :meth:`DataFrame.set_axis` and :meth:`Series.set_axis` (other than ``"labels"``) (:issue:`41485`)
diff --git a/pandas/core/dtypes/cast.py b/pandas/core/dtypes/cast.py
index 8a230e5da01dc..5c7211a5d1852 100644
--- a/pandas/core/dtypes/cast.py
+++ b/pandas/core/dtypes/cast.py
@@ -2036,7 +2036,7 @@ def construct_1d_ndarray_preserving_na(
 
 def maybe_cast_to_integer_array(
     arr: list | np.ndarray, dtype: np.dtype, copy: bool = False
-):
+) -> np.ndarray:
     """
     Takes any dtype and returns the casted version, raising for when data is
     incompatible with integer/unsigned integer dtypes.
@@ -2107,6 +2107,20 @@ def maybe_cast_to_integer_array(
     if is_float_dtype(arr.dtype) or is_object_dtype(arr.dtype):
         raise ValueError("Trying to coerce float values to integers")
 
+    if casted.dtype < arr.dtype:
+        # GH#41734 e.g. [1, 200, 923442] and dtype="int8" -> overflows
+        warnings.warn(
+            f"Values are too large to be losslessly cast to {dtype}. "
+            "In a future version this will raise OverflowError. To retain the "
+            f"old behavior, use pd.Series(values).astype({dtype})",
+            FutureWarning,
+            stacklevel=find_stack_level(),
+        )
+        return casted
+
+    # No known cases that get here, but raising explicitly to cover our bases.
+    raise ValueError(f"values cannot be losslessly cast to {dtype}")
+
 
 def convert_scalar_for_putitemlike(scalar: Scalar, dtype: np.dtype) -> Scalar:
     """
diff --git a/pandas/tests/frame/test_stack_unstack.py b/pandas/tests/frame/test_stack_unstack.py
index 4a7c4faade00d..b617514f383af 100644
--- a/pandas/tests/frame/test_stack_unstack.py
+++ b/pandas/tests/frame/test_stack_unstack.py
@@ -358,7 +358,7 @@ def test_unstack_preserve_dtypes(self):
                 "E": Series([1.0, 50.0, 100.0]).astype("float32"),
                 "F": Series([3.0, 4.0, 5.0]).astype("float64"),
                 "G": False,
-                "H": Series([1, 200, 923442], dtype="int8"),
+                "H": Series([1, 200, 923442]).astype("int8"),
             }
         )
 
diff --git a/pandas/tests/series/test_constructors.py b/pandas/tests/series/test_constructors.py
index f03322f9b0d6c..9376bd5f025b3 100644
--- a/pandas/tests/series/test_constructors.py
+++ b/pandas/tests/series/test_constructors.py
@@ -711,6 +711,21 @@ def test_constructor_cast(self):
         with pytest.raises(ValueError, match=msg):
             Series(["a", "b", "c"], dtype=float)
 
+    def test_constructor_signed_int_overflow_deprecation(self):
+        # GH#41734 disallow silent overflow
+        msg = "Values are too large to be losslessly cast"
+        with tm.assert_produces_warning(FutureWarning, match=msg):
+            ser = Series([1, 200, 923442], dtype="int8")
+
+        expected = Series([1, -56, 50], dtype="int8")
+        tm.assert_series_equal(ser, expected)
+
+        with tm.assert_produces_warning(FutureWarning, match=msg):
+            ser = Series([1, 200, 923442], dtype="uint8")
+
+        expected = Series([1, 200, 50], dtype="uint8")
+        tm.assert_series_equal(ser, expected)
+
     def test_constructor_unsigned_dtype_overflow(self, uint_dtype):
         # see gh-15832
         msg = "Trying to coerce negative values to unsigned integers"