The 6-foot-2, 197-pound quarterback is transferring from Santa Monica College. He originally signed with Washington out of high school and spent two seasons in the program, redshirting in 2013 and playing five games in 2014.
Williams threw for 2,750 yards with 31 touchdowns and four interceptions in 2015.
Freshman Chase Hansen was thought to be the heir apparent, but he switched to safety midway through the season and his future position is now in question.
Williams is planning to enroll in school for the spring semester.