I don't agree that men or women decide to keep an affair 'secret' for reasons of returning home should their new romance fail. What husband/wife would accept a returning spouse - for any reason?
I can totally see the benefit of 'keeping quiet' because if you didn't confess at the start of an affair, blurting it out at the end of a relationship isn't going to make the other person feel any better, is it? Why can't people be free to just end their relationships without a full-blown autopsy? All that telling the partner of the 'other person' would bring is unhealthy comparison. I know that there are posters who disagree with this and think full disclosure is the only way but, not their call, it's OP's call, the MM's call, nobody else's, not even the other partners involved.
If a relationship is over then it's over. It only needs one of the pair to decide that. It's up to the leaving partner to decide what they tell, how much they tell, etc. The important bit is to actually tell the other person that it is over. This, they have done.
Living... read Thisisaghostlyeuphemism's post carefully. I think she's right about the fact that you ought to be pulling right away at the moment, concentrate on your other relationships/friendships. I said in a previous post that you're not starting from quite the same position as anybody else getting together with somebody. You're not - this is it, the 'pinch point' - and it needs careful handling if you really think this is going somewhere. I think that you should both be taking a little time to reflect on your ended relationships - not necessarily grieve them, people make all kinds of assumptions about the need for that - but just reflection and thinking about how you will not bring past mistakes to your next relationship. You have all the time in the world now, the rest of your lives, there's no rush.