Brewer was projected to start for the Red Raiders last season, but a summer back injury kept him from the playing the first month of the season. When he finally returned from the injury, freshmen Davis Webb and Baker Mayfield had solidified their places on the depth chart ahead of him.
Brewer originally had sought a transfer to TCU or Texas, but Texas Tech denied him a release to transfer within the Big 12.
He will join a wide-open competition at Virginia Tech to replace Logan Thomas. The Hokies have several quarterbacks on scholarship, including fifth-year senior Mark Leal, though none with much experience.
As for the Red Raiders, they will go into the spring with just one scholarship quarterback in Webb. Incoming freshman Patrick Mahomes will immediately become the backup when he arrives on campus in the summer.