First and foremost, congratulations on your engagement!! How very exciting for you!
As for advice, I'm not sure how qualified I am to give any, but here goes.
I would definately not tell them to mind their own business!! Go visit with them in person, and tell them that you have something you need to discuss with them that is very important to you. That way they aren't completely blown away by the news. Make sure and tell them that you love them and respect their opinion, but you honestly feel this is the only man for you and you can't give up on him just to please them. Explain about how he treats you and about what a wonderful person he is, and tell them how important it is that you have their blessing.
You may or may not want to bring him along, depending on what your parents are like. If you prefer to go it alone, maybe bring a gift for them from him. Definately prepare what you want to say, and I would emphasize how important both your parents and your fiance are to you. You probably know your parents well enough to know what will pull at their heartstrings.
Definately try and get them together at some point so your parents can get to know him. If they refuse to budge on their stance, at least try and convince them to get to know him before they decide. But try your best not to make it a situation where they feel you are choosing between them and him.
I'm not sure if this makes as much sense as I wanted it to. I guess my main point is to not make it confrontational, just let them know how much you love them and him, and how important it is to you that they get along. Handle yourself like an adult and try not to give any ultimatums.
I wish you the absolute best of luck, and congratulations again!