diff --git a/doc/source/user_guide/timeseries.rst b/doc/source/user_guide/timeseries.rst
index 3fd6fe67772bc..6df234a027ee9 100644
--- a/doc/source/user_guide/timeseries.rst
+++ b/doc/source/user_guide/timeseries.rst
@@ -2102,19 +2102,14 @@ The ``period`` dtype can be used in ``.astype(...)``. It allows one to change th
    # change monthly freq to daily freq
    pi.astype("period[D]")
 
+   # convert to DatetimeIndex
+   pi.astype("datetime64[ns]")
+
    # convert to PeriodIndex
    dti = pd.date_range("2011-01-01", freq="M", periods=3)
    dti
    dti.astype("period[M]")
 
-.. deprecated:: 1.4.0
-    Converting PeriodIndex to DatetimeIndex with ``.astype(...)`` is deprecated and will raise in a future version. Use ``obj.to_timestamp(how).tz_localize(dtype.tz)`` instead.
-
-.. ipython:: python
-
-    # convert to DatetimeIndex
-    pi.to_timestamp(how="start")
-
 PeriodIndex partial string indexing
 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
diff --git a/doc/source/whatsnew/v1.4.0.rst b/doc/source/whatsnew/v1.4.0.rst
index a76077e8b46c1..58f3fee1805d7 100644
--- a/doc/source/whatsnew/v1.4.0.rst
+++ b/doc/source/whatsnew/v1.4.0.rst
@@ -537,7 +537,6 @@ Other Deprecations
 - Deprecated casting behavior when passing an item with mismatched-timezone to :meth:`DatetimeIndex.insert`, :meth:`DatetimeIndex.putmask`, :meth:`DatetimeIndex.where` :meth:`DatetimeIndex.fillna`, :meth:`Series.mask`, :meth:`Series.where`, :meth:`Series.fillna`, :meth:`Series.shift`, :meth:`Series.replace`, :meth:`Series.reindex` (and :class:`DataFrame` column analogues). In the past this has cast to object dtype. In a future version, these will cast the passed item to the index or series's timezone (:issue:`37605`,:issue:`44940`)
 - Deprecated the 'errors' keyword argument in :meth:`Series.where`, :meth:`DataFrame.where`, :meth:`Series.mask`, and :meth:`DataFrame.mask`; in a future version the argument will be removed (:issue:`44294`)
 - Deprecated the ``prefix`` keyword argument in :func:`read_csv` and :func:`read_table`, in a future version the argument will be removed (:issue:`43396`)
-- Deprecated :meth:`PeriodIndex.astype` to ``datetime64[ns]`` or ``DatetimeTZDtype``, use ``obj.to_timestamp(how).tz_localize(dtype.tz)`` instead (:issue:`44398`)
 - Deprecated passing non boolean argument to sort in :func:`concat` (:issue:`41518`)
 - Deprecated passing arguments as positional for :func:`read_fwf` other than ``filepath_or_buffer`` (:issue:`41485`):
 - Deprecated passing ``skipna=None`` for :meth:`DataFrame.mad` and :meth:`Series.mad`, pass ``skipna=True`` instead (:issue:`44580`)
@@ -676,6 +675,7 @@ Conversion
 - Bug in :meth:`DataFrame.astype` not propagating ``attrs`` from the original :class:`DataFrame` (:issue:`44414`)
 - Bug in :meth:`DataFrame.convert_dtypes` result losing ``columns.names`` (:issue:`41435`)
 - Bug in constructing a ``IntegerArray`` from pyarrow data failing to validate dtypes (:issue:`44891`)
+- Bug in :meth:`Series.astype` not allowing converting from a ``PeriodDtype`` to ``datetime64`` dtype, inconsistent with the :class:`PeriodIndex` behavior (:issue:`45038`)
 -
 
 Strings
diff --git a/pandas/core/arrays/period.py b/pandas/core/arrays/period.py
index 6112ccccb89ff..487b51735bd4e 100644
--- a/pandas/core/arrays/period.py
+++ b/pandas/core/arrays/period.py
@@ -53,6 +53,7 @@
 from pandas.core.dtypes.common import (
     TD64NS_DTYPE,
     ensure_object,
+    is_datetime64_any_dtype,
     is_datetime64_dtype,
     is_dtype_equal,
     is_float_dtype,
@@ -666,6 +667,12 @@ def astype(self, dtype, copy: bool = True):
                 return self.copy()
         if is_period_dtype(dtype):
             return self.asfreq(dtype.freq)
+
+        if is_datetime64_any_dtype(dtype):
+            # GH#45038 match PeriodIndex behavior.
+            tz = getattr(dtype, "tz", None)
+            return self.to_timestamp().tz_localize(tz)
+
         return super().astype(dtype, copy=copy)
 
     def searchsorted(
diff --git a/pandas/core/indexes/period.py b/pandas/core/indexes/period.py
index 8dcd379a4eb9b..aba834a47ffef 100644
--- a/pandas/core/indexes/period.py
+++ b/pandas/core/indexes/period.py
@@ -358,14 +358,9 @@ def astype(self, dtype, copy: bool = True, how=lib.no_default):
 
         if is_datetime64_any_dtype(dtype):
             # 'how' is index-specific, isn't part of the EA interface.
-            # GH#44398 deprecate astype(dt64), matching Series behavior
-            warnings.warn(
-                f"Converting {type(self).__name__} to DatetimeIndex with "
-                "'astype' is deprecated and will raise in a future version. "
-                "Use `obj.to_timestamp(how).tz_localize(dtype.tz)` instead.",
-                FutureWarning,
-                stacklevel=find_stack_level(),
-            )
+            # GH#45038 implement this for PeriodArray (but without "how")
+            #  once the "how" deprecation is enforced we can just dispatch
+            #  directly to PeriodArray.
             tz = getattr(dtype, "tz", None)
             return self.to_timestamp(how=how).tz_localize(tz)
 
diff --git a/pandas/tests/arrays/period/test_astype.py b/pandas/tests/arrays/period/test_astype.py
index 52cd28c8d5acc..e16220acd3210 100644
--- a/pandas/tests/arrays/period/test_astype.py
+++ b/pandas/tests/arrays/period/test_astype.py
@@ -66,5 +66,12 @@ def test_astype_period():
 def test_astype_datetime(other):
     arr = period_array(["2000", "2001", None], freq="D")
     # slice off the [ns] so that the regex matches.
-    with pytest.raises(TypeError, match=other[:-4]):
-        arr.astype(other)
+    if other == "timedelta64[ns]":
+        with pytest.raises(TypeError, match=other[:-4]):
+            arr.astype(other)
+
+    else:
+        # GH#45038 allow period->dt64 because we allow dt64->period
+        result = arr.astype(other)
+        expected = pd.DatetimeIndex(["2000", "2001", pd.NaT])._data
+        tm.assert_datetime_array_equal(result, expected)
diff --git a/pandas/tests/indexes/period/methods/test_astype.py b/pandas/tests/indexes/period/methods/test_astype.py
index c44f2efed1fcc..e2340a2db02f7 100644
--- a/pandas/tests/indexes/period/methods/test_astype.py
+++ b/pandas/tests/indexes/period/methods/test_astype.py
@@ -164,10 +164,7 @@ def test_period_astype_to_timestamp(self):
         assert res.freq == exp.freq
 
         exp = DatetimeIndex(["2011-01-01", "2011-02-01", "2011-03-01"], tz="US/Eastern")
-        msg = "Use `obj.to_timestamp"
-        with tm.assert_produces_warning(FutureWarning, match=msg):
-            # GH#44398
-            res = pi.astype("datetime64[ns, US/Eastern]")
+        res = pi.astype("datetime64[ns, US/Eastern]")
         tm.assert_index_equal(res, exp)
         assert res.freq == exp.freq
 
diff --git a/pandas/tests/indexes/test_common.py b/pandas/tests/indexes/test_common.py
index 0407dc02833fd..50770f5bb38f2 100644
--- a/pandas/tests/indexes/test_common.py
+++ b/pandas/tests/indexes/test_common.py
@@ -393,9 +393,6 @@ def test_astype_preserves_name(self, index, dtype):
         ):
             # This astype is deprecated in favor of tz_localize
             warn = FutureWarning
-        elif isinstance(index, PeriodIndex) and dtype == "datetime64[ns]":
-            # Deprecated in favor of to_timestamp GH#44398
-            warn = FutureWarning
         try:
             # Some of these conversions cannot succeed so we use a try / except
             with tm.assert_produces_warning(warn):