Jones takes the job a day after sources said he declined an offer to become the new coach at Colorado. A six-year contract was finalized early Friday, sources told ESPN.
Cincinnati said Jones had resigned his position with the Bearcats effective immediately.
At Tennessee, the 44-year-old Jones will succeed Derek Dooley, who was fired Nov. 18 after going 15-21 in three years. Dooley posted a losing record in each of his three seasons at Tennessee, the first time since 1909-11 the Volunteers have finished below .500 three straight years.
Friday's news caps a whirlwind week for Jones.
The Denver Post reported Wednesday that Jones had accepted a five-year, $13.5 million offer from Colorado before Jones denied the report.