Acceptance With Displeasure. It's possible that your boss won't take immediate action like the reaction above__but will make it clear that he or she isn't exactly happy about your resignation. Maybe, for example, she'll mutter a curt, "Thank you for letting me know," followed by two weeks of obvious displeasure or denial that you're leaving__through gruff comments ("You know, you're really leaving us in the lurch") or a refusal to interact with you more than absolutely necessary.
After that, you're ready to close out your letter and move on. The basic closings are fine here__again, you don't need to go overly sentimental or formal, but you should also write as if it will be read by anyone at the company. And with that signing flourish, you're done! You've resigned, and you're ready for your exciting new job.