As suspected, Microsoft has finally addressed the DRM issue with content you’ve purchased on your Xbox 360. In the past, if you bought a new console you couldn’t transfer the licenses—one customer was told by an Xbox 360 CSR to “buy the content again.” Now you can visit this page on xbox.com and transfer your licenses to a new console. Hooray for progress!
It’s a simple two-part process. First, you must transfer your authorized licenses here on the site. Second, you must download the transferred licenses onto your new Xbox 360.
Microsoft points out that if you’ve sent your Xbox 360 in for repair or replacement, “the licenses have already been transferred as part of the repair process, and you do not need to use the license transfer tool, but you may need to download the content again.”
“Transferring Content Licenses to a New Console” (Thanks to Justin!)