Jones will receive a raise of more than $250,000 on his new contract.
After beating Vanderbilt last week in their regular season finale, the Volunteers finished 6-6 to become bowl eligible in Jones' second season at the school. Tennessee finished 5-7 in 2013 in his first year.
Michigan fired head coach Brady Hoke on Tuesday after the Wolverines finished 5-7 and failed to qualify for a bowl for the first time since 2009. During four seasons at Michigan, Hoke compiled a 31-20 record.
Prior to becoming Tennessee's coach, Jones was in charge at Cincinnati for three years, compiling a 23-14 record. He went 19-6 in his final two seasons with the Bearcats.
His first head coaching job came at Central Michigan in 2007. He finished 27-13 in three seasons at the school, including an 11-2 mark in his final season.
- Paul Palladino