Olsen transferred from SUU to BYU after an LDS Church mission to Mexico City in 2010-11.
The 6-foot-3, 209-pounder is transferring because he wants the opportunity to play more, and with Hill the unquestioned starter the next two years, barring injury, prospects for doing that at BYU appear slim for Olsen.
Olsen appeared in just four games last season and attempted just three passes. He completed one pass for 4 yards, against Idaho State, and carried the ball once for 4 yards.
He redshirted his first season in Provo, 2012, after returning from his church mission.
Coincidentally, the last quarterback to transfer from BYU to SUU, Brad Sorensen, had a standout career at the Cedar City school and is now in the NFL as a backup for the San Diego Chargers.
In his first stint at SUU, in 2009, Olsen played in six games as a freshman and completed 8 of 14 passes for 115 yards and two touchdowns.
Christian Stewart, a transfer from Snow College who played high school football at nearby Timpanogos High, was the third-string quarterback in 2013 and likely moves up to the backup role for his senior season. Another possible backup is Billy Green of Woodway, Wash., who will be a sophomore this upcoming season.