Barnes' contract at Tennessee is for six years, with a base salary of $2.25 million per season. Barnes will be introduced at a press conference at 4 p.m. Eastern on Tuesday.
Texas announced on Sunday that Barnes and the Longhorns mutually agreed to part ways after 17 seasons.
"Rick Barnes is an elite basketball coach in every respect," Tennessee athletic director Dave Hart said. "Rick brings an extremely impressive track record of excellence, as well as much-needed stability, to our men's basketball program. This is an exciting day for our Tennessee family."
Last week, the Volunteers fired coach Donnie Tyndall after only one season at the school amid allegations of NCAA violations committed while he was the head coach at Southern Mississippi.
Barnes is the winningest coach in Texas basketball history. He led the Longhorns to the Final Four in 2003 and has 604 career wins, 402 of which came in those 17 seasons at Texas. He previously coached at George Mason, Providence and Clemson.
Tennessee finished 16–16 this season, coming in 10th in the SEC.
- Molly Geary and Scooby Axson