Been there, done that, or rather had it done to me. Don't tell her you cheated. It will only make her feel worse. Do tell her you don't love her like a lifetime, but you respect her enough to quit being an asshole to try and drive her away. That is why you are telling her. Then don't do the comfort sex thing for the next three months till you find another warm body.
The cheating was not cool. But it would be even more uncool to tell her and use that as the reason/wedge/whatever to break up. It's over. Tell her the real reason, that you don't love her. Leave out the hurtful behaviour part. She'll deal.
Odrade