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.
Even those that require you give a certain amount of "notice" before you quit your current job (two_week notice is standard) often may not provide any formal requirement that you do so by writing a letter of resignation or explain in detail why you're leaving.