diff --git a/Lib/asyncio/unix_events.py b/Lib/asyncio/unix_events.py
index 17fb4d5f7646ce..a2680865ed968f 100644
--- a/Lib/asyncio/unix_events.py
+++ b/Lib/asyncio/unix_events.py
@@ -394,6 +394,9 @@ def _sock_sendfile_native_impl(self, fut, registered_fd, sock, fileno,
                 fut.set_result(total_sent)
                 return
 
+        # On 32-bit architectures truncate to 1GiB to avoid OverflowError
+        blocksize = min(blocksize, sys.maxsize//2 + 1)
+
         try:
             sent = os.sendfile(fd, fileno, offset, blocksize)
         except (BlockingIOError, InterruptedError):
diff --git a/Misc/NEWS.d/next/Library/2023-07-22-16-44-58.gh-issue-82500.cQYoPj.rst b/Misc/NEWS.d/next/Library/2023-07-22-16-44-58.gh-issue-82500.cQYoPj.rst
new file mode 100644
index 00000000000000..065394fd6ee712
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2023-07-22-16-44-58.gh-issue-82500.cQYoPj.rst
@@ -0,0 +1 @@
+Fix overflow on 32-bit systems with :mod:`asyncio` :func:`os.sendfile` implemention.