diff --git a/doc/source/whatsnew/v2.0.0.rst b/doc/source/whatsnew/v2.0.0.rst
index 331c2421a31ef4..0e6d1029d352b4 100644
--- a/doc/source/whatsnew/v2.0.0.rst
+++ b/doc/source/whatsnew/v2.0.0.rst
@@ -548,6 +548,8 @@ Removal of prior version deprecations/changes
 - Changed behavior of setitem-like operations (``__setitem__``, ``fillna``, ``where``, ``mask``, ``replace``, ``insert``, fill_value for ``shift``) on an object with :class:`DatetimeTZDtype` when using a value with a non-matching timezone, the value will be cast to the object's timezone instead of casting both to object-dtype (:issue:`44243`)
 - Changed behavior of :class:`Index`, :class:`Series`, :class:`DataFrame` constructors with floating-dtype data and a :class:`DatetimeTZDtype`, the data are now interpreted as UTC-times instead of wall-times, consistent with how integer-dtype data are treated (:issue:`45573`)
 - Changed behavior of :class:`Series` and :class:`DataFrame` constructors with integer dtype and floating-point data containing ``NaN``, this now raises ``IntCastingNaNError`` (:issue:`40110`)
+- Changed behavior of :class:`Series` and :class:`DataFrame` constructors with an integer ``dtype`` and values that are too large to losslessly cast to this dtype, this now raises ``ValueError`` (:issue:`41734`)
+- Changed behavior of :class:`Series` and :class:`DataFrame` constructors with an integer ``dtype`` and values having either ``datetime64`` or ``timedelta64`` dtypes, this now raises ``TypeError``, use ``values.view("int64")`` instead (:issue:`41770`)
 - Removed the deprecated ``base`` and ``loffset`` arguments from :meth:`pandas.DataFrame.resample`, :meth:`pandas.Series.resample` and :class:`pandas.Grouper`. Use ``offset`` or ``origin`` instead (:issue:`31809`)
 - Changed behavior of :meth:`Series.fillna` and :meth:`DataFrame.fillna` with ``timedelta64[ns]`` dtype and an incompatible ``fill_value``; this now casts to ``object`` dtype instead of raising, consistent with the behavior with other dtypes (:issue:`45746`)
 - Change the default argument of ``regex`` for :meth:`Series.str.replace` from ``True`` to ``False``. Additionally, a single character ``pat`` with ``regex=True`` is now treated as a regular expression instead of a string literal. (:issue:`36695`, :issue:`24804`)
diff --git a/pandas/core/dtypes/cast.py b/pandas/core/dtypes/cast.py
index 215b6c1021fd89..11c2bf8711ad14 100644
--- a/pandas/core/dtypes/cast.py
+++ b/pandas/core/dtypes/cast.py
@@ -41,7 +41,6 @@
     IntCastingNaNError,
     LossySetitemError,
 )
-from pandas.util._exceptions import find_stack_level
 from pandas.util._validators import validate_bool_kwarg
 
 from pandas.core.dtypes.common import (
@@ -1680,25 +1679,17 @@ def maybe_cast_to_integer_array(
 
     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(),
+        raise ValueError(
+            f"Values are too large to be losslessly converted to {dtype}. "
+            f"To cast anyway, use pd.Series(values).astype({dtype})"
         )
-        return casted
 
     if arr.dtype.kind in ["m", "M"]:
         # test_constructor_maskedarray_nonfloat
-        warnings.warn(
-            f"Constructing Series or DataFrame from {arr.dtype} values and "
-            f"dtype={dtype} is deprecated and will raise in a future version. "
-            "Use values.view(dtype) instead.",
-            FutureWarning,
-            stacklevel=find_stack_level(),
+        raise TypeError(
+            f"Constructing a Series or DataFrame from {arr.dtype} values and "
+            f"dtype={dtype} is not supported. Use values.view({dtype}) instead."
         )
-        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}")
diff --git a/pandas/tests/frame/test_constructors.py b/pandas/tests/frame/test_constructors.py
index b83e060a666500..b6c6792355fc78 100644
--- a/pandas/tests/frame/test_constructors.py
+++ b/pandas/tests/frame/test_constructors.py
@@ -1054,18 +1054,15 @@ def test_constructor_maskedarray_nonfloat(self):
         assert isna(frame).values.all()
 
         # cast type
-        msg = r"datetime64\[ns\] values and dtype=int64"
-        with tm.assert_produces_warning(FutureWarning, match=msg):
+        msg = r"datetime64\[ns\] values and dtype=int64 is not supported"
+        with pytest.raises(TypeError, match=msg):
             with warnings.catch_warnings():
                 warnings.filterwarnings(
                     "ignore",
                     category=DeprecationWarning,
                     message="elementwise comparison failed",
                 )
-                frame = DataFrame(
-                    mat, columns=["A", "B", "C"], index=[1, 2], dtype=np.int64
-                )
-        assert frame.values.dtype == np.int64
+                DataFrame(mat, columns=["A", "B", "C"], index=[1, 2], dtype=np.int64)
 
         # Check non-masked values
         mat2 = ma.copy(mat)
diff --git a/pandas/tests/series/test_constructors.py b/pandas/tests/series/test_constructors.py
index 826ad20dfd54e2..b44f5b699cab49 100644
--- a/pandas/tests/series/test_constructors.py
+++ b/pandas/tests/series/test_constructors.py
@@ -749,25 +749,17 @@ 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"
+    def test_constructor_signed_int_overflow_raises(self):
+        # GH#41734 disallow silent overflow, enforced in 2.0
+        msg = "Values are too large to be losslessly converted"
         numpy_warning = DeprecationWarning if is_numpy_dev else None
-        with tm.assert_produces_warning(
-            (FutureWarning, numpy_warning), match=msg, check_stacklevel=False
-        ):
-            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, numpy_warning), match=msg, check_stacklevel=False
-        ):
-            ser = Series([1, 200, 923442], dtype="uint8")
+        with pytest.raises(ValueError, match=msg):
+            with tm.assert_produces_warning(numpy_warning):
+                Series([1, 200, 923442], dtype="int8")
 
-        expected = Series([1, 200, 50], dtype="uint8")
-        tm.assert_series_equal(ser, expected)
+        with pytest.raises(ValueError, match=msg):
+            with tm.assert_produces_warning(numpy_warning):
+                Series([1, 200, 923442], dtype="uint8")
 
     @pytest.mark.parametrize(
         "values",