A formal announcement was expected early next week, said the person, who requested anonymity because the deal had not been finalized.
Kiffin, 33, replaces Phillip Fulmer, who was forced out after 17 seasons as Vols coach. Fulmer won a national championship in 1998 but had two losing seasons in the last five years, including a 4-7 mark this year.
Tennessee athletic department spokeswoman Tiffany Carpenter declined to comment on Kiffin because Fulmer had not finished his season. Athletic director Mike Hamilton did not return a phone message seeking comment.
The Vols (3-7, 2-5 Southeastern Conference) host Kentucky (6-5, 2-5) on Saturday night in what has been dubbed "Phillip Fulmer appreciation day."
The Knoxville News Sentinel first reported the deal.
Kiffin was the youngest coach in the NFL's modern history when hired to lead the Raiders in January 2007 at age 31.
The son of longtime NFL defensive coordinator Monte Kiffin had a rocky relationship with Oakland owner Al Davis, who fired him Sept. 30 for what he said was insubordination. Kiffin had a 5-15 record with the Raiders.
He's since filed a grievance with the NFL to claim salary he maintains he's owed by the team.
Kiffin spent seven seasons as an assistant at Southern California under coach Pete Carroll, including two as recruiting and offensive coordinator.
