As a graduate transfer, he will be eligible immediately.
Minshew had earlier announced that he would transfer to Alabama. A source close to Minshew told ESPN's Adam Rittenberg that the announcement was essentially to get attention from other schools and he was never likely to go to Tuscaloosa.
Minshew started five games for the Pirates last season, throwing for 2,140 yards and 16 touchdowns. He withdrew from the school after graduating after the fall semester.
At WSU, he will join a program that is mourning the loss of projected starter Tyler Hilinski, who committed suicide in January. The Cougars are light on experience at the position, and Minshew figures to compete with true freshman Cammon Cooper and juniors Trey Tinsley and Anthony Gordon for the starting job.