diff --git a/doc/source/whatsnew/v3.0.0.rst b/doc/source/whatsnew/v3.0.0.rst
index e621ab2a5b9c5..07f5b01709223 100644
--- a/doc/source/whatsnew/v3.0.0.rst
+++ b/doc/source/whatsnew/v3.0.0.rst
@@ -544,6 +544,7 @@ I/O
 - Bug in :class:`DataFrame` and :class:`Series` ``repr`` of :py:class:`collections.abc.Mapping`` elements. (:issue:`57915`)
 - Bug in :meth:`DataFrame.to_dict` raises unnecessary ``UserWarning`` when columns are not unique and ``orient='tight'``. (:issue:`58281`)
 - Bug in :meth:`DataFrame.to_excel` when writing empty :class:`DataFrame` with :class:`MultiIndex` on both axes (:issue:`57696`)
+- Bug in :meth:`DataFrame.to_stata` when writing :class:`DataFrame` and ``byteorder=`big```. (:issue:`58969`)
 - Bug in :meth:`DataFrame.to_string` that raised ``StopIteration`` with nested DataFrames. (:issue:`16098`)
 - Bug in :meth:`read_csv` raising ``TypeError`` when ``index_col`` is specified and ``na_values`` is a dict containing the key ``None``. (:issue:`57547`)
 - Bug in :meth:`read_stata` raising ``KeyError`` when input file is stored in big-endian format and contains strL data. (:issue:`58638`)
diff --git a/pandas/io/stata.py b/pandas/io/stata.py
index 9c6cd2faeaa2f..d1e57ad568ba5 100644
--- a/pandas/io/stata.py
+++ b/pandas/io/stata.py
@@ -3037,6 +3037,8 @@ def __init__(
         if byteorder is None:
             byteorder = sys.byteorder
         self._byteorder = _set_endianness(byteorder)
+        # Flag whether chosen byteorder matches the system on which we're running
+        self._native_byteorder = self._byteorder == _set_endianness(sys.byteorder)
 
         gso_v_type = "I"  # uint32
         gso_o_type = "Q"  # uint64
@@ -3049,13 +3051,20 @@ def __init__(
             o_size = 6
         else:  # version == 119
             o_size = 5
-        self._o_offet = 2 ** (8 * (8 - o_size))
+        if self._native_byteorder:
+            self._o_offet = 2 ** (8 * (8 - o_size))
+        else:
+            self._o_offet = 2 ** (8 * o_size)
         self._gso_o_type = gso_o_type
         self._gso_v_type = gso_v_type
 
     def _convert_key(self, key: tuple[int, int]) -> int:
         v, o = key
-        return v + self._o_offet * o
+        if self._native_byteorder:
+            return v + self._o_offet * o
+        else:
+            # v, o will be swapped when applying byteorder
+            return o + self._o_offet * v
 
     def generate_table(self) -> tuple[dict[str, tuple[int, int]], DataFrame]:
         """
@@ -3532,7 +3541,9 @@ def _convert_strls(self, data: DataFrame) -> DataFrame:
         ]
 
         if convert_cols:
-            ssw = StataStrLWriter(data, convert_cols, version=self._dta_version)
+            ssw = StataStrLWriter(
+                data, convert_cols, version=self._dta_version, byteorder=self._byteorder
+            )
             tab, new_data = ssw.generate_table()
             data = new_data
             self._strl_blob = ssw.generate_blob(tab)
diff --git a/pandas/tests/io/test_stata.py b/pandas/tests/io/test_stata.py
index bf17e62985fe9..2534df6a82f89 100644
--- a/pandas/tests/io/test_stata.py
+++ b/pandas/tests/io/test_stata.py
@@ -1678,7 +1678,8 @@ def test_date_parsing_ignores_format_details(self, column, datapath):
         formatted = df.loc[0, column + "_fmt"]
         assert unformatted == formatted
 
-    def test_writer_117(self, temp_file):
+    @pytest.mark.parametrize("byteorder", ["little", "big"])
+    def test_writer_117(self, byteorder, temp_file):
         original = DataFrame(
             data=[
                 [
@@ -1736,6 +1737,7 @@ def test_writer_117(self, temp_file):
         original.to_stata(
             path,
             convert_dates={"datetime": "tc"},
+            byteorder=byteorder,
             convert_strl=["forced_strl"],
             version=117,
         )
@@ -1940,7 +1942,8 @@ def test_stata_119(self, datapath):
                 assert reader._nvar == 32999
 
     @pytest.mark.parametrize("version", [118, 119, None])
-    def test_utf8_writer(self, version, temp_file):
+    @pytest.mark.parametrize("byteorder", ["little", "big"])
+    def test_utf8_writer(self, version, byteorder, temp_file):
         cat = pd.Categorical(["a", "β", "ĉ"], ordered=True)
         data = DataFrame(
             [
@@ -1968,6 +1971,7 @@ def test_utf8_writer(self, version, temp_file):
             convert_strl=["strls"],
             variable_labels=variable_labels,
             write_index=False,
+            byteorder=byteorder,
             version=version,
             value_labels=value_labels,
         )