Instructions
Navigate to the Xbox License Transfer page on your PC using your Internet browser (see Resources).
Click "Start the License Transfer Process Now" at the bottom of the page. Sign into Xbox.com using your Xbox 360 user name and password. Click "Next" at the bottom of the screen. You are then prompted to turn on your Xbox 360.
Turn on the Xbox 360 that you are transferring the licenses to and sign in with the profile that the downloaded content was purchased on. Click "Next" on the website on the PC once complete.
Click "Confirm." The licenses are transferred to your new console. The process takes a few minutes depending on your Internet speed and the amount of licenses to transfer.
Press the silver "Guide" button in the middle of your Xbox 360 controller to access the Xbox 360's menu.
Select "Settings," followed by "Account Management" and "Download History."
Highlight each item and select "Download Again." The download is updated with the new license, allowing you to play your content both offline and online. Repeat this for each piece of downloaded content.