Stoops becomes the 28th coach in the school's history and his hiring ends a nine-week search that began after John Mackovic was fired on Sept. 28.
"I'm obviously very excited about the opportunity to become a head coach and lead my own program, and pleased to be working with a great administrative group that has shown its support for football," Stoops said. "I think the quality of the people with whom I've been dealing in the hiring process is one of the compelling reasons I took the job."
Stoops, who turns 42 next week, runs the defense for the top-ranked Sooners with Brent Venables and also serves as associate head coach. He is the youngest head football coach at Arizona since Larry Smith was hired in 1980 at the age of 40.
Arizona finished a dismal 2-10 with a 28-7 loss to Arizona State on Friday, settling for a first-ever 10th-place finish in the Pac-10.