Can I  tell my old friends girlfriend that he's been cheating their entire relationship?
That is quite a huge mess to get into, are you really ready to disclose that information? She might like to hear it.
Because he's being an asshole to me.
That is understandable, you want revenge. I think he deserves to be exposed now that you mention it. But really think about it, what will it really solve? If it something worth it or not, that is. Its up to you though.
I'm going to do this anyway. It's not my fault if the schmuck cheats.
I guess you could argue that you have a duty to your friend to expose a cheater. It's like having a win-win situation where getting back at your friend will also show him your loyalty. I guess if you do it casually, it might be in your best interest, but just make sure you talk to him when he is fully calm and relaxed.