I found out he was cheating and now im moving out without telling him. Am i doing the right thing?

ok i girls i need your help on this one. me and my boyfriend have been knowing each other for 4 years and have been together for 1 year and some change. when we 1st met each other we were just friends with benefits and it was cool with me because i didnt want a boyfriend at the time. but before we hooked up i was like do you have a girlfriend and he was like no im single. so did our thing. . anyway, i started getting ims from a girl and she finally told me that he was her boyfriend and that they lived together with his mom and had been together for 3 years. so never the less i left him alone. well later on down the line i ran into him longstory short we got together and he even moved in. i started going through his yahoo and found out he was sleeping around with her. this was in jan. so i got me an apartment and i am moving with out telling him next weekend . so my question is girls am i doing the right thing? there is so much more to this story. just e-mail me and i will tell you .