Smart and Muschamp were teammates at Georgia and colleagues on coaching staffs at Valdosta State and LSU.
Muschamp's role will be that of an off-field coach. Smart said Muschamp will "help coach the coaches" and work on the defensive side of the ball.
"It's very valuable to have a guy who has been a head coach at two places in our conference," Smart said. "He knows the ins and outs of this conference. He'll be able to help our staff, our coaches, in a lot of ways. I'm excited to have him join us."
Muschamp was fired by South Carolina in November with three games remaining in his fifth season as head coach. The terms of Muschamp's contract called for a buyout of around $15 million.