I had this situation come up recently with another pair of schools, and the advice I got from several people (including post-docs who have recently been on both sides of these things) has been to mention in a brief but polite e-mail that I am VERY excited to have been invited, but that I am unable to attend the interview day because I have already accepted an invitation to interview at another institution. She recommended that I mention that I was going to another interview so that it doesn't just look like I'm flaking out, going on vacation, etc. etc. That there is a legitimate good reason I can't come. I did this, asked if there were other arrangements that could be made, there were, no one was upset, and I have an in-person interview scheduled for a different day.
Good luck! And congratulations!!