I know you are probably quite hurt, but he isn't trying to hurt you...In fact, he's probably trying to make it as painless as possible for you...It's possible that he thinks it would be easier for you to move on if it is a clean break without ties...His approach might not be the best approach, but in heartbreak moments like that, there isn't really an easy and painless exit...He has sex with you because he is still sexually attracted to you...But now that you know, it is up to you if you want to confront the situation calmly so you can rationally move forward or let your anger eat you alive...

Angie's my yin......
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Grow up. All you want to do is have a fight, right? Admit it. If you had any maturity, you'd have resolved or talked about the "rocky relations" with him and resolved it some time ago. He's leaving because things remain unresolved you're unwilling to budge...
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Ask him if he's planning on leaving (since you were snooping in his computer) and NEGOTIATE a mutually agreeable parting of the ways. It's skill that I'm guessing is going to come in handy for you...
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Carlos..

I'm gonna say he has every right to tell you when he's ready to tell you...If he's cheating, then kick him out...Otherwise, he should be able to stay until he's ready to tell you he wants to leave...

If he's planning to break up with you, shouldn't he discuss it with you first? How the hell did you find out? Has he been talking to everyone else about it? If he had confided in someone surely they would do their upmost to ensure that it didn't get back to you.. You need to talk to him face to face. Tonight. If he wants to break up, then he can move out. Obviously if he has no where to go you can't just dump him and his stuff on the street, but I'm sure he has some friend he can crash with until he gets himself sorted. Talk to him, maybe it was a misunderstanding, maybe he was only talking to someone about you guys going through a bad patch....

It's definitely time to confront him on this. You have a right to know if he plans on leaving you, and why...