A good relationship with one's brother is pretty special, so I'm glad to hear you want to make amends for your past actions. But keep in mind this broken trust will take a a long time to completely heal.
At this point I think the best thing for you to do is just be a friend. If you've had experiences at university maybe you could offer some tips on how to deal with all the newness and difficulties that university life is going to bring. If you can offer any kind of financial help (without it seeming to intrude) that could be a plus. If you can offer help with studies that's always welcome for any student. Any healing that will begin on his part will originate with him. You can't force the issue and/or demand that the issue be dealt with NOW. Many times just being there, and just listening with a genuine sense of understanding is all that's needed.
I don't see how telling your mother right now would improve the situation for her, you or your brother. That's not to say, never tell. There may be some future time when that's ideal.
You didn't mention this as an item on your agenda of things to do, but I hope you are giving some thought to your own healing and recovery. This is in no way an accusation or judgement, but when you say, "I've made peace of sorts with my own abuse" what exactly does this mean. There are hundreds of members here who've used denial and brushing aside as ways to cope with abuse. And it never has worked.
Don't be too hard on yourself. You deserve a life free from the guilt, shame, self-loathing and humiliation that abuse brings with it. And your brother does too.
Peace and Best wishes as you heal.
Never, never, never, never give up...Winston Churchill