In general I agree with Patricia Shanahan's answer to do it in two separate steps, but with one important extra piece of advice. The first time you meet him, don't tell him you've already accepted the other offer.
If I was your brother, the thing that I would dislike the most about this wouldn't really be the decision to leave and to "betray" him and his company, but rather the fact that it comes out of the blue. One day you are working for him as you've always been doing, and on the following day you are leaving? Now this is something that would irritate me.
Since you two have a very close personal relationship, and since you both care about it, in your place I would have informed him about the offer before accepting it, discussing it with him, explaining why it is interesting for you (and if you think money is too "vulgar" as a reason, concentrate on the other things, especially those your brother can't really make a counter-proposal about, like your wife's desire to move there), and even looking for advice. Now it's too late for doing this, but you can still make it look like it. So, tell him you've just got an offer and that you are considering that option.
Do state openly that you are kinda torn apart: on the one side there's him, on the other one there's this offer which really looks interesting. By the way, did the other company contact you on their initiative (e.g. they got your name through your university), or did you actively apply for that job? In any case I'd tell him the former. Look, it isn't my fault, it's them who sent me this offer, and now I'm tempted!
If your brother is the reasonable person you say he is, realizing how much better this offer is for you, he might even end up encouraging you to take it ("I'd be sorry if you left, and even more if you moved to another town, but hey, this really looks like a great opportunity for you, and it'd be a shame if you missed it!"). Or he might not, and he might try to keep you there. Then you can tell him that you don't know what to do and you need some time to think about it. In that case, wait a couple of days and tell him you've decided to accept the offer. Even if he isn't happy with this decision, at least it won't come as a complete surprise.
I realize lying to one's brother isn't a nice thing, but considering it would be a way to try avoiding some friction in what is a delicate situation, it's what I'd call an innocent lie, and I don't think it would be so bad.