The 79-year-old Snyder decided to step away Sunday, a day after the Wildcats finished a 5-7 season with a disheartening loss to Iowa State that eliminated them from bowl eligibility.
The school announced that a search for his replacement would begin immediately.
Snyder turned around one of the worst programs in college football when he arrived in 1988, making it a perennial powerhouse in the Big 12. He finishes his career with a record of 215-117-1, trips to 19 bowl games, two Big 12 championships and a spot in college football's Hall of Fame.
Along the way, he overcame throat cancer, sent dozens of players to the NFL and gave countless assistants a path to becoming head coaches.