A Professional Greeting. Your letter should be addressed to your boss. There's a good chance that this letter will merely end up in a file in HR, but it starts with your boss. Assuming this is someone with whom you work reasonably close with on a daily basis, it doesn't have to be super stiff and formal. Specific and professional is the right tone here.
However, I'm happy to help out however I can in the next two weeks." If you haven't landed a new gig yet or your new start date is negotiable, know your limits. If you're willing to stay an additional three weeks, for example, don't let your manager talk you into staying three more months.