My boyfriend cheated on me.. what should I do?

Ash
My boyfriend and I have been together off and on for 4 years, there's been a lot of woman in the past but anytime there was another woman, we weren't together. This one particular time we are together and he cheated on me with his ex girlfriend. His ex girlfriend decided to message me on twitter the other day and tell me all about it. Sending me screenshots, telling me the dates etc. When I questioned him about it he lied to me for a whole day then the next morning finally told me the truth.Also he came over my house crying like real tears and squeezed me telling me how sorry he was, he'll do anything to make it right, he only wants me etc.. but idk I'm confused. Should I forgive him and move on hoping he'll be better after our talk. Or just give up. 
 

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