diff --git a/pandas/core/dtypes/cast.py b/pandas/core/dtypes/cast.py
index 9580ab1b520e0b..4e0a04942feaef 100644
--- a/pandas/core/dtypes/cast.py
+++ b/pandas/core/dtypes/cast.py
@@ -1025,6 +1025,8 @@ def convert_dtypes(
     -------
     np.dtype, or ExtensionDtype
     """
+    from pandas.core.arrays.string_ import StringDtype
+
     inferred_dtype: str | DtypeObj
 
     if (
@@ -1103,6 +1105,13 @@ def convert_dtypes(
             # If we couldn't do anything else, then we retain the dtype
             inferred_dtype = input_array.dtype
 
+    elif (
+        convert_string
+        and isinstance(input_array.dtype, StringDtype)
+        and input_array.dtype.na_value is np.nan
+    ):
+        inferred_dtype = pandas_dtype_func("string")
+
     else:
         inferred_dtype = input_array.dtype
 
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index 259e969112dd75..5b04bc3ced849b 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -657,7 +657,12 @@ def convert(
             convert_non_numeric=True,
         )
         refs = None
-        if copy and res_values is values:
+        if (
+            copy
+            and res_values is values
+            or isinstance(res_values, NumpyExtensionArray)
+            and res_values._ndarray is values
+        ):
             res_values = values.copy()
         elif res_values is values:
             refs = self.refs
diff --git a/pandas/tests/frame/methods/test_convert_dtypes.py b/pandas/tests/frame/methods/test_convert_dtypes.py
index 59779234b46d91..e7f6e5d625d3ec 100644
--- a/pandas/tests/frame/methods/test_convert_dtypes.py
+++ b/pandas/tests/frame/methods/test_convert_dtypes.py
@@ -3,21 +3,15 @@
 import numpy as np
 import pytest
 
-from pandas._config import using_string_dtype
-
 import pandas as pd
 import pandas._testing as tm
 
 
 class TestConvertDtypes:
-    # TODO convert_dtypes should not use NaN variant of string dtype, but always NA
-    @pytest.mark.xfail(using_string_dtype(), reason="TODO(infer_string)")
     @pytest.mark.parametrize(
         "convert_integer, expected", [(False, np.dtype("int32")), (True, "Int32")]
     )
-    def test_convert_dtypes(
-        self, convert_integer, expected, string_storage, using_infer_string
-    ):
+    def test_convert_dtypes(self, convert_integer, expected, string_storage):
         # Specific types are tested in tests/series/test_dtypes.py
         # Just check that it works for DataFrame here
         df = pd.DataFrame(
@@ -182,7 +176,6 @@ def test_convert_dtypes_pyarrow_timestamp(self):
         result = expected.convert_dtypes(dtype_backend="pyarrow")
         tm.assert_series_equal(result, expected)
 
-    @pytest.mark.xfail(using_string_dtype(), reason="TODO(infer_string)")
     def test_convert_dtypes_avoid_block_splitting(self):
         # GH#55341
         df = pd.DataFrame({"a": [1, 2, 3], "b": [4, 5, 6], "c": "a"})
@@ -197,7 +190,6 @@ def test_convert_dtypes_avoid_block_splitting(self):
         tm.assert_frame_equal(result, expected)
         assert result._mgr.nblocks == 2
 
-    @pytest.mark.xfail(using_string_dtype(), reason="TODO(infer_string)")
     def test_convert_dtypes_from_arrow(self):
         # GH#56581
         df = pd.DataFrame([["a", datetime.time(18, 12)]], columns=["a", "b"])
diff --git a/pandas/tests/io/parser/dtypes/test_dtypes_basic.py b/pandas/tests/io/parser/dtypes/test_dtypes_basic.py
index da17999bba4cad..5138dfb61eaac1 100644
--- a/pandas/tests/io/parser/dtypes/test_dtypes_basic.py
+++ b/pandas/tests/io/parser/dtypes/test_dtypes_basic.py
@@ -463,7 +463,6 @@ def test_dtype_backend_and_dtype(all_parsers):
     tm.assert_frame_equal(result, expected)
 
 
-@pytest.mark.xfail(using_string_dtype(), reason="TODO(infer_string)", strict=False)
 def test_dtype_backend_string(all_parsers, string_storage):
     # GH#36712
     pa = pytest.importorskip("pyarrow")
@@ -507,7 +506,6 @@ def test_dtype_backend_ea_dtype_specified(all_parsers):
     tm.assert_frame_equal(result, expected)
 
 
-@pytest.mark.xfail(using_string_dtype(), reason="TODO(infer_string)", strict=False)
 def test_dtype_backend_pyarrow(all_parsers, request):
     # GH#36712
     pa = pytest.importorskip("pyarrow")
diff --git a/pandas/tests/series/methods/test_convert_dtypes.py b/pandas/tests/series/methods/test_convert_dtypes.py
index 46fed9032c13d5..c2cc838619790c 100644
--- a/pandas/tests/series/methods/test_convert_dtypes.py
+++ b/pandas/tests/series/methods/test_convert_dtypes.py
@@ -230,9 +230,9 @@ def test_convert_dtypes(
             and params[0]
             and not params[1]
         ):
-            # If we would convert with convert strings then infer_objects converts
-            # with the option
-            expected_dtype = "string[pyarrow_numpy]"
+            # If convert_string=False and infer_objects=True, we end up with the
+            # default string dtype instead of preserving object for string data
+            expected_dtype = pd.StringDtype(na_value=np.nan)
 
         expected = pd.Series(data, dtype=expected_dtype)
         tm.assert_series_equal(result, expected)