Originally Posted by pidgeon92
However, if these books are acquired from Amazon and have DRM, this will not work, as the files are DRMd to whichever device you downloaded them for.
In this case, you will want to go to your Kindle's archive, and download them from there. Alternately, you can go to your Amazon.com account on the web, and go to Manage Your Kindle, and send each book from there to your new Kindle.
Non DRM mobi books can be sent via email to your Kindle. You will need WiFi access.