Muschamp replaces Urban Meyer, who resigned abruptly Wednesday but will still coach the team in the Jan. 1 Outback Bowl.
Muschamp has been the defensive coordinator for the Texas Longhorns since 2008 and was the "head coach in waiting" under Mack Brown.
He has also served as the defensive coordinator for Auburn and Louisiana State, as well as with the Miami Dolphins of the NFL.
"Texas is an unbelievable place that I'm really proud that I was able to be a part of," Muschamp said. "I really enjoyed working with the coaches, staff and all of the kids. It's just a great place with tremendous people."
Muschamp, 39, was in line to receive a five-year deal as Texas's head coach once Brown stepped down, but Brown instead signed an extension to stay in Austin through the 2016 season.