Tennessee is looking to replace Derek Dooley, who was fired Nov. 18 after three seasons leading the Volunteers. Tennessee was 15-21 overall and 4-19 in the SEC under Dooley. The Volunteers were 4-7 overall and 0-7 in the league in 2012.
Louisville is ranked No. 18 after a 10-2 season and will play in the Sugar Bowl after winning the Big East Conference's automatic bowl bid.
"It was the toughest decision I've ever had to make in my 29 years of coaching," Strong said of choosing between Louisville and Tennessee. "It was a life decision for myself, my family and my school."
Strong said he appreciated that Louisville Athletics Director Tom Jurich gave him his first head coaching position after 27 years as an assistant.
Louisville is 24-14 in three seasons with Strong as coach.
Oklahoma State Coach Mike Gundy Wednesday refused an offer to take over the Tennessee program.