Oklahoma reportedly fired Norvell and co-offensive coordinator Josh Heupel after Norvell served as an offensive assistant with the school since 2008, including co-offensive coordinator since December 2010.
This season Oklahoma ranked 23rd nationally at 464.7 yards per game and was tied for 20th in the country in scoring offense with 36.4 points per game. Prior to his stint at Oklahoma, Norvell served as an assistant for multiple college and NFL teams, including UCLA in 2007.
"The first thing that really drew me to this opportunity was the chance to work with Charlie Strong," Norvell said in a news release. "I've followed his career for a long time, and after sitting down and talking to him, seeing his vision for the program, the recruiting philosophy, his values, every area of the team, I was totally impressed. Our visit convinced me I wanted to be a part of that championship vision at Texas.
"Charlie and I have a lot in common. I believe in developing young people on and off the field. I'm a very disciplined person, love my players, and I pour myself into them every day. I could really feel and see that in Charlie when he talked about the team and the players."
Norvell will replace Les Koenning, who was reportedly fired along with tight ends coach Bruce Chambers in late December.
Texas (6-7) this season ranked ninth in the Big 12 in total offense at 337.3 yards per game and ninth in scoring offense with 21.4 points per game.
The Longhorns also finished last in the conference in passing yards per game (199.9).