Your packet will go to a review board, assuming physical and everything is already done. Then you get a board review and the surgeon general officially awards you the scholarship and you get a letter. If your MCAT was over 28, then you are an automatic acceptance, so its all just a formality.
After you get your scholarship award letter, then you have to sign the contract, take your oath of office and wait for school to start. My advice: once you sign your contract, call the recruiter's office at least once a week to check the status and find out if you need to sign anything else. Amazingly, I had several forms that needed updating throughout the process, but noone ever called ME, it was always the other way around. Just keep on it and you'll be fine. Also, once your paperwork is in, it would be a good idea to get your military id, as this is a pain and you won't have as much time to sit in the office and wait once school starts.
Good luck.