diff --git a/Tests/test_file_jpeg2k.py b/Tests/test_file_jpeg2k.py
index cd142e67f..0229b2243 100644
--- a/Tests/test_file_jpeg2k.py
+++ b/Tests/test_file_jpeg2k.py
@@ -252,6 +252,20 @@ def test_mct():
             assert_image_similar(im, jp2, 1.0e-3)
 
 
+def test_sgnd(tmp_path):
+    outfile = str(tmp_path / "temp.jp2")
+
+    im = Image.new("L", (1, 1))
+    im.save(outfile)
+    with Image.open(outfile) as reloaded:
+        assert reloaded.getpixel((0, 0)) == 0
+
+    im = Image.new("L", (1, 1))
+    im.save(outfile, signed=True)
+    with Image.open(outfile) as reloaded_signed:
+        assert reloaded_signed.getpixel((0, 0)) == 128
+
+
 def test_rgba():
     # Arrange
     with Image.open("Tests/images/rgb_trns_ycbc.j2k") as j2k:
diff --git a/docs/handbook/image-file-formats.rst b/docs/handbook/image-file-formats.rst
index c9e32835a..a41ef7cf8 100644
--- a/docs/handbook/image-file-formats.rst
+++ b/docs/handbook/image-file-formats.rst
@@ -568,6 +568,11 @@ The :py:meth:`~PIL.Image.Image.save` method supports the following options:
     encoded using RLCP mode will have increasing resolutions decoded as they
     arrive, and so on.
 
+**signed**
+    If true, then tell the encoder to save the image as signed.
+
+    .. versionadded:: 9.4.0
+
 **cinema_mode**
     Set the encoder to produce output compliant with the digital cinema
     specifications.  The options here are ``"no"`` (the default),
diff --git a/docs/releasenotes/9.4.0.rst b/docs/releasenotes/9.4.0.rst
index aae3e2b64..e4e1e40fe 100644
--- a/docs/releasenotes/9.4.0.rst
+++ b/docs/releasenotes/9.4.0.rst
@@ -45,6 +45,12 @@ removes the hidden RGB values for better compression by default in libwebp 0.5
 or later. By setting this option to ``True``, the encoder will keep the hidden
 RGB values.
 
+Added ``signed`` option when saving JPEG2000
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+If the ``signed`` keyword argument is present and true when saving JPEG2000
+images, then tell the encoder to save the image as signed.
+
 Added IFD, Interop and LightSource ExifTags enums
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
diff --git a/src/PIL/Jpeg2KImagePlugin.py b/src/PIL/Jpeg2KImagePlugin.py
index c67d8d6bf..11d1d488a 100644
--- a/src/PIL/Jpeg2KImagePlugin.py
+++ b/src/PIL/Jpeg2KImagePlugin.py
@@ -321,6 +321,7 @@ def _save(im, fp, filename):
     progression = info.get("progression", "LRCP")
     cinema_mode = info.get("cinema_mode", "no")
     mct = info.get("mct", 0)
+    signed = info.get("signed", False)
     fd = -1
 
     if hasattr(fp, "fileno"):
@@ -342,6 +343,7 @@ def _save(im, fp, filename):
         progression,
         cinema_mode,
         mct,
+        signed,
         fd,
     )
 
diff --git a/src/encode.c b/src/encode.c
index e6352cbfe..21c42d915 100644
--- a/src/encode.c
+++ b/src/encode.c
@@ -1212,11 +1212,12 @@ PyImaging_Jpeg2KEncoderNew(PyObject *self, PyObject *args) {
     char *cinema_mode = "no";
     OPJ_CINEMA_MODE cine_mode;
     char mct = 0;
+    int sgnd = 0;
     Py_ssize_t fd = -1;
 
     if (!PyArg_ParseTuple(
             args,
-            "ss|OOOsOnOOOssbn",
+            "ss|OOOsOnOOOssbbn",
             &mode,
             &format,
             &offset,
@@ -1231,6 +1232,7 @@ PyImaging_Jpeg2KEncoderNew(PyObject *self, PyObject *args) {
             &progression,
             &cinema_mode,
             &mct,
+            &sgnd,
             &fd)) {
         return NULL;
     }
@@ -1329,6 +1331,7 @@ PyImaging_Jpeg2KEncoderNew(PyObject *self, PyObject *args) {
     context->progression = prog_order;
     context->cinema_mode = cine_mode;
     context->mct = mct;
+    context->sgnd = sgnd;
 
     return (PyObject *)encoder;
 }
diff --git a/src/libImaging/Jpeg2K.h b/src/libImaging/Jpeg2K.h
index d030b0c43..b28a0440a 100644
--- a/src/libImaging/Jpeg2K.h
+++ b/src/libImaging/Jpeg2K.h
@@ -85,6 +85,9 @@ typedef struct {
     /* Set multiple component transformation */
     char mct;
 
+    /* Signed */
+    int sgnd;
+
     /* Progression order (LRCP/RLCP/RPCL/PCRL/CPRL) */
     OPJ_PROG_ORDER progression;
 
diff --git a/src/libImaging/Jpeg2KEncode.c b/src/libImaging/Jpeg2KEncode.c
index fe5511ba5..db1c5c0c9 100644
--- a/src/libImaging/Jpeg2KEncode.c
+++ b/src/libImaging/Jpeg2KEncode.c
@@ -343,7 +343,7 @@ j2k_encode_entry(Imaging im, ImagingCodecState state) {
         image_params[n].x0 = image_params[n].y0 = 0;
         image_params[n].prec = prec;
         image_params[n].bpp = bpp;
-        image_params[n].sgnd = 0;
+        image_params[n].sgnd = context->sgnd == 0 ? 0 : 1;
     }
 
     image = opj_image_create(components, image_params, color_space);