Instructions
Click the "Sign In" link in the top-right corner of the page of xbox.com/drm. Log in with the Windows Live account connected to your gamer tag.
Click the "Start the license transfer process now" link. On the resulting page, you will see all of the licenses associated with your account. Click "Next."
Sign in to Xbox Live on the new Xbox. When you are logged in, the console will be identified as the one you wish to transfer the licenses to. Click "Next."
Click "Confirm" on the resulting "Confirm Transfer" page on the Xbox. The licenses are now associated with the new console.
Go to Xbox LIVE Marketplace and select "Account Management, Download History." Select the license and click "Download Again" to download the license into your console.