My suggestion to you is, that you should contact the other woman. Obviously it's bugging you, and on the contrary to what people are saying here, a lot of the times the people who are being cheated on have no idea, or if they do suspect something, no evidence.
If you do decide to tell this woman, you should go all out and not just send some randomly vague message saying something like: "Sorry to tell you but your boyfriend's cheating on you. He did it with me, so I know." These kinds of vague messages are easily explained by the cheater as some lunatic's bad-mouthing. I know this, because two of my friends have actually at some point received messages like these, and both of the times their boyfriends managed to satisfy their suspicions. On one of the times, he was caught cheating later, and in the other case she's now married to him even though she has seen strong evidence later on (such as sex messages that he has sent out from a fake Fb profile to other women), but refuses to believe them now that they have kids etc.
If you have evidence (photos, text messages, Facebook messages, dates marked down) you should provide them. Tell her kindly and with apologies, that you have been contemplating about how/if to contact her, but that a while ago you had a relationship with her boyfriend. Tell her very straight-forwardly that he denied having a gf, and when you later asked about it, he lied and told she was just a friend. You should also make it clear that there was sexual involvement (if there actually was), this way he can't weasel out and say that nothing actually happened between you two.
Before doing this, I think you should also brace yourself that she might not take this very well, and might in fact blame you for it. Especially if she decides to stay with him even despite you contacting her (blaming you is just a way for her to cope). If you are willing to endure the possibility of being the "bad guy", I would say go for it. If you live in different cities, it shouldn't matter that much anyway.
You can console yourself that at least you tried to spare her from the possible drawbacks of living with a dick: finding out about the cheating after popping out a couple of kids or getting and STD for instance.