diff --git a/Lib/_pyio.py b/Lib/_pyio.py
--- a/Lib/_pyio.py
+++ b/Lib/_pyio.py
@@ -1857,6 +1857,19 @@ class TextIOWrapper(TextIOBase):
         return buffer
 
     def seek(self, cookie, whence=0):
+        def _reset_encoder(position):
+            """Reset the encoder (merely useful for proper BOM handling)"""
+            try:
+                encoder = self._encoder or self._get_encoder()
+            except LookupError:
+                # Sometimes the encoder doesn't exist
+                pass
+            else:
+                if position != 0:
+                    encoder.setstate(0)
+                else:
+                    encoder.reset()
+
         if self.closed:
             raise ValueError("tell on closed file")
         if not self._seekable:
@@ -1877,6 +1890,7 @@ class TextIOWrapper(TextIOBase):
             self._snapshot = None
             if self._decoder:
                 self._decoder.reset()
+            _reset_encoder(position)
             return position
         if whence != 0:
             raise ValueError("unsupported whence (%r)" % (whence,))
@@ -1914,17 +1928,7 @@ class TextIOWrapper(TextIOBase):
                 raise OSError("can't restore logical file position")
             self._decoded_chars_used = chars_to_skip
 
-        # Finally, reset the encoder (merely useful for proper BOM handling)
-        try:
-            encoder = self._encoder or self._get_encoder()
-        except LookupError:
-            # Sometimes the encoder doesn't exist
-            pass
-        else:
-            if cookie != 0:
-                encoder.setstate(0)
-            else:
-                encoder.reset()
+        _reset_encoder(cookie)
         return cookie
 
     def read(self, size=None):
diff --git a/Lib/test/test_io.py b/Lib/test/test_io.py
--- a/Lib/test/test_io.py
+++ b/Lib/test/test_io.py
@@ -2577,6 +2577,19 @@ class TextIOWrapperTest(unittest.TestCas
             with self.open(filename, 'rb') as f:
                 self.assertEqual(f.read(), 'bbbzzz'.encode(charset))
 
+    def test_seek_append_bom(self):
+        # Same test, but first seek to the start and then to the end
+        filename = support.TESTFN
+        for charset in ('utf-8-sig', 'utf-16', 'utf-32'):
+            with self.open(filename, 'w', encoding=charset) as f:
+                f.write('aaa')
+            with self.open(filename, 'a', encoding=charset) as f:
+                f.seek(0)
+                f.seek(0, self.SEEK_END)
+                f.write('xxx')
+            with self.open(filename, 'rb') as f:
+                self.assertEqual(f.read(), 'aaaxxx'.encode(charset))
+
     def test_errors_property(self):
         with self.open(support.TESTFN, "w") as f:
             self.assertEqual(f.errors, "strict")
diff --git a/Modules/_io/textio.c b/Modules/_io/textio.c
--- a/Modules/_io/textio.c
+++ b/Modules/_io/textio.c
@@ -2041,11 +2041,10 @@ static int
 }
 
 static int
-_textiowrapper_encoder_setstate(textio *self, cookie_type *cookie)
+_textiowrapper_encoder_reset(textio *self, int start_of_stream)
 {
     PyObject *res;
-    /* Same as _textiowrapper_decoder_setstate() above. */
-    if (cookie->start_pos == 0 && cookie->dec_flags == 0) {
+    if (start_of_stream) {
         res = PyObject_CallMethodObjArgs(self->encoder, _PyIO_str_reset, NULL);
         self->encoding_start_of_stream = 1;
     }
@@ -2060,6 +2059,14 @@ static int
     return 0;
 }
 
+static int
+_textiowrapper_encoder_setstate(textio *self, cookie_type *cookie)
+{
+    /* Same as _textiowrapper_decoder_setstate() above. */
+    return _textiowrapper_encoder_reset(
+        self, cookie->start_pos == 0 && cookie->dec_flags == 0);
+}
+
 static PyObject *
 textiowrapper_seek(textio *self, PyObject *args)
 {
@@ -2127,7 +2134,17 @@ textiowrapper_seek(textio *self, PyObjec
         }
 
         res = _PyObject_CallMethodId(self->buffer, &PyId_seek, "ii", 0, 2);
-        Py_XDECREF(cookieObj);
+        Py_CLEAR(cookieObj);
+        if (res == NULL)
+            goto fail;
+        if (self->encoder) {
+            /* If seek() == 0, we are at the start of stream, otherwise not */
+            cmp = PyObject_RichCompareBool(res, _PyIO_zero, Py_EQ);
+            if (cmp < 0 || _textiowrapper_encoder_reset(self, cmp)) {
+                Py_DECREF(res);
+                goto fail;
+            }
+        }
         return res;
     }
     else if (whence != 0) {