Well you've done a pretty horrible thing to your boyfriend. Make him feel like he's all paranoid about you & this guy, then probably guilty that he didn't trust you...then cheat on him with the guy. That said I'm not here to play judge, jury and executioner because I believe everyone makes mistakes...even really huge ones.
Unfortunately I would say the only course of action is to break this news to your boyfriend. Otherwise it will always be at the back of your mind & may well make you start to feel pretty negative about yourself.
As for the chances of the relationship continuing. Obviously it depends on your man, but cheating on someone will often permanently affect the balance of your relationship. You will always feel like the black sheep of the pairing & he may never look at you the same way again. I'd say the more likely outcome is that you will break up, but at least if you do you'll have a clear conscience.