Prepare for It. This one is easy. All you have to do is smile and say "Thank you so much for your support. I've enjoyed my time here and I've learned a lot from you. Let me know what I can do to make the transition easier." Are you always going to get reaction number five? Probably not. But if you look for the signs, you can likely anticipate your boss' response, go into the conversation prepared, and come out stronger on the other side. Then, you can breathe a sign of relief and start looking forward to starting your new position.
The Hand_off. Finally, state your willingness to help out with the transition. You don't need to go into great detail (and definitely don't promise anything you can't deliver), but a couple of lines stating that you'll ensure a smooth wrap_up of your duties will show that you're in the game until the very end. Obviously, feel free to adjust this a bit based on your experience and your company culture, then submit it via the typical procedures at your company.