This looks like the explanatory の （like のだ・のです・んだ・んです）. (It is used to mark that the information answers an actual or anticipated question, i.e., "I'm not just saying this just for fun, but to explain something", and tends to have an emphatic effect).
However, the following copula is converted to a conjunctive form で so that the usual でもいい form for "it is okay/good/fine if" can be used.
So, although I'd need to see more context to be sure, this probably means something along the lines of:
It is okay, even if I will (end up) teaching him "from 1 to 10!"
The speaker might be reassuring the listener that even if it is a lot of effort, he is willing to teach the learner in detail, or something along those lines. The exact nuance is hard to tell without context, since explanatory の interacts heavily with the 'outer' context, but if I had to guess, maybe the listener worries that the learner is a beginner, and expressed worry that the teacher doesn't know what he's getting himself into!
Note that a past-tense "I've (already) taught him everything" doesn't really make much sense with the でもいい portion, and 教える isn't in past-tense form, so I would rule out a past-tense translation. If it was "I've already taught him everything so it is fine", I would expect something using ので・から and so forth, like 俺は彼にもう一から十まで教えたんだから、平気だ.