diff --git a/distributed/worker.py b/distributed/worker.py
index 3b365af6c6..31ead8f395 100644
--- a/distributed/worker.py
+++ b/distributed/worker.py
@@ -2,6 +2,7 @@
 import bisect
 import errno
 import heapq
+import io
 import logging
 import os
 import random
@@ -12,9 +13,9 @@
 import weakref
 from collections import defaultdict, deque, namedtuple
 from collections.abc import MutableMapping
-from contextlib import suppress
+from contextlib import suppress  ExitStack, redirect_stdout
 from datetime import timedelta
-from functools import partial
+from functools import partial, wraps
 from inspect import isawaitable
 from pickle import PicklingError
 
@@ -3721,6 +3722,20 @@ def weight(k, v):
     return sizeof(v)
 
 
+def log_stdout(func):
+    @wraps(func)
+    def wrapped(*args, **kwargs):
+        with ExitStack() as stack:
+            out, _ = io.StringIO(), io.StringIO()
+            stack.enter_context(redirect_stdout(out))
+            try:
+                return func(*args, **kwargs)
+            finally:
+                logger.info(out.getvalue())
+
+    return wrapped
+
+
 async def run(server, comm, function, args=(), kwargs=None, is_coro=None, wait=True):
     kwargs = kwargs or {}
     function = pickle.loads(function)
@@ -3743,12 +3758,12 @@ async def run(server, comm, function, args=(), kwargs=None, is_coro=None, wait=T
     logger.info("Run out-of-band function %r", funcname(function))
     try:
         if not is_coro:
-            result = function(*args, **kwargs)
+            result = log_stdout(function)(*args, **kwargs)
         else:
             if wait:
-                result = await function(*args, **kwargs)
+                result = await log_stdout(function)(*args, **kwargs)
             else:
-                server.loop.add_callback(function, *args, **kwargs)
+                server.loop.add_callback(log_stdout(function), *args, **kwargs)
                 result = None
 
     except Exception as e: