I can't see this having been posted before. I tried this yesterday and it is a great tool! I have had about 4 Xboxes in the past (I usually take them back for an exchange at the store, saves time) and can confirm that all my arcade games now work offline as well as online! More info below.
Got a new Xbox 360®? Great. But maybe you downloaded games or other content from Xbox LIVE® Marketplace onto an older Xbox 360, and now you want all that content on your new system. Well, now there's a way to do it.
With the license transfer tool, you can easily transfer the licenses of all your previously downloaded content from your old console to the new one.
Follow the instructions here: http://www.xbox.com/en-GB/support/drm/