Well my close friend is moving close to like literally across the street. The only problem I see is that everybody knew we were together and even my parents but now her boyfriend and her is moving close to me. I already know what's going to happen people going to be like. I seen her with this dude blah blah blahhh. What should I do tell everybody that's she's moving closer to me?

He's her boyfriend, so what's this 'I seen her with this dude?' Of course they'll see them together, and they'll be living together. Are you worried that you are losing her friendship? Hopefully not, but it does happen. Try not to worry unless it happens, and don't even bother with what to tell people - don't tell them anything.

So let everybody find out their own way?

Yes. You don't have to be secretive if someone asks, but you don't have to broadcast it either, or people will be more aware of how it's bothering you.
Getting a boyfriend means less time with you, but moving closer means more time with you. And if they have an argument or she just wants to complain about him? There you are, across the street. You never know until you know though.