Levis transferred to Kentucky this offseason after playing three seasons at Penn State, where he played as both a quarterback and running back.
In announcing the decision, Stoops praised Levis' efficiency running the offense.
"He won the job," Stoops said.
Levis played in eight games last season, starting once. During that time, Levis completed 33 of 55 passes for 421 yards and a score. He also rushed the ball 82 times for 260 yards and three touchdowns.
Levis beat out former Auburn transfer Joey Gatewood to become the starter. Stoops said that Gatewood informed him that he intended to transfer.
Kentucky is scheduled to open the season at home against UL-Monroe on Sept. 4.