You said domain registration, and not hosting.
Currently it sounds like you're paying for the registration, and paying for the hosting. If you want to completely turn over a domain registration and its hosting, the recipient will first need to set up a hosting account here. They will have to pay full price (no promo code) if they want to host what used to be your domain here. This prevents discount hopping.
I'd then initiate a Reg. Transfer for the domain registration itself. While I'm waiting for that to process, I'd back up all site data (files and database). Support will need to get involved, as existing domains can't be re-hosted here on a different account without intervention. Support may even be able to transfer the data, but I wouldn't count on it.