Pruitt, 43, has been the defensive coordinator with the Crimson Tide for the past two seasons. Alabama is ranked first nationally in scoring defense this season and second in total defense.
ESPN reported that Pruitt intends to stay with the Crimson Tide through the College Football Playoff. Fourth-ranked Alabama plays No. 1 Clemson in the Sugar Bowl on New Year's Day.
A two-time Broyles Award finalist as the top assistant coach in college football, Pruitt served as a defensive backs coach in Tuscaloosa from 2007-2012 before being named as the defensive coordinator at Florida State in 2013. He then was the defensive coordinator at Georgia in 2014-15 before returning to his alma mater.
Pruitt will become the fifth head coach at Tennessee in the past 11 years. He replaces Butch Jones, who was fired after posting a 34-27 overall mark, including 14-24 in SEC play, during a five-year span.
The move to hire Pruitt would end a chaotic stretch in which Tennessee came close to hiring Ohio State defensive coordinator Greg Schiano in late November. The school and Schiano agreed to a deal on Nov. 26, but the Volunteers backed out after fan backlash.
Tennessee's coaching search then ranged from Oklahoma State's Mike Gundy, Duke's David Cutcliffe, Purdue's Jeff Brohm, North Carolina State's Dave Doeren and Washington State's Mike Leach until athletic director John Currie was fired last week.
The school hired former football coach Phillip Fulmer to take Currie's place on Friday.