Well, you'd better get started, I'd say. Springing it on them at the last minute isn't going to cut it. This is an extreme move, no matter how you try to spin it. I guarantee they will be upset; your sole hope is for them to be not 100% upset, and for them to be flexible and reasonable and open to convincing. They might not be, no matter what you do.
You will need to make it abundantly clear that this is a good move (it is, isn't it?), you'll have a support system (you will, won't you?), and you'll be financially secure (right?). You have to make it clear that you will visit when you can (you will, right?) and you will even help them financially if they want to visit you and can't afford it (yes?).
The other side of the world is a helluva move. And I have to say, they would be right to be concerned about it, and beyond their own personal emotions. This is a place where it's quite the production to get there and back again. Three states away? You can drive, or take a train, bus, or plane, at least part of the way. But Guam is a long, long flight, and not a cheap one.
Guam is also not a place that's known for any sort of industry. It is a dot in the middle of the Pacific Ocean. Even Hawaii and Japan are pretty far slogs from it. Making your money off tourism means you live at the whims of the American and Japanese economies. Wikipedia (not always the greatest of sources, I will admit) says the biggest employer is United Airlines. But let's face it; there are plenty of other places you can be and still work for United. And if your heart is set on working in the tourism industry, you can do that in a lot of other places, too.
The second-biggest employer is the US military. Is this for a deployment? Because I don't think you would know where deployment would be this far in advance. As for making your living off the military, then you're confined to whatever relates to that, whether it's running a restaurant or a nearby hotel. US military bases are still all over the world, and many of them are in far more accessible locales.
Pacific beauty comes in a lot of other places; Hawaii is a far more reasonable trip although it's not a cheap place to live, by any means, and it suffers from similar issues of being remote and claustrophobic, but at least there are other islands you can hop to. With Guam, your (somewhat) local options are confined to Micronesia.
Also, being that far away (and you are not going there to be with anyone in your family, or any of your friends, so far as I can tell from your post), means that you will be overly dependent upon your boyfriend for companionship, friendship, and entertainment. He will be the one to take you to the Emergency Room if necessary. He will be the one to take you shopping, too, or to a day spa or whatever you want to do with your time while there and not working. It will be a ton of togetherness. You may feel you are truly in love and all of that, but even people who love each other deeply need a break from each other every now and then. Being that remote, and without friends already there, means you need to make friends, fast, when you get there, in order to try to build a support system.
BTW, I don't know if it matters to you, but you may also be walking straight into a situation where you'd be a minority. Are you Filipino or of other Asian descent? Are you Roman Catholic? Because if you aren't one or of the other of these characteristics, you're less than 10% of the population, and probably less than 5%.
Think about how you're going to answer all of these concerns and questions before you say anything to your parents. And think about whether you really mean the answers, or whether you're just looking to convince them of the rightness of your actions.
Because you need to be convinced, too. And being in love is not a good enough reason.