Thank you all for the replies/encouragement on this thread.
I just had a talk with my brother, and even though I was VERY nervous, it actually went much better than I thought.
I simply told him that we had some things coming up and we'd be needing our space back. He asked if I had a timeline, and I told him October 1st. He said that was plenty of time.
I told him that it had nothing to do with me being mad or anything, because I wasn't.
He told me he'd start looking right away, and that he'd really like to find a place that had another bedroom so his son could have his own room when he's with my brother.
Even though I'm really worried about him, and hope that he won't have trouble finding a place, he didn't act like it was a big worry, which is good.
I'm having mixed feelings right now. Part of me is relieved that we've talked, and it will be nice to have our space back. The other part of me is sad, because he really is a good brother who I love very much, and I'll miss him.