Cooks joined the Oklahoma staff in 2015 after a stint at Notre Dame. The last two years, he's also been the assistant defensive coordinator.
The secondary struggled this season, as Oklahoma was last among the 129 FBS programs in passing yards allowed. Texas Tech, Cooks' new program, was No. 128.
Cooks' departure leaves at least two vacancies on the Sooners' defensive staff. Linebackers coach Tim Kish announced his retirement last week.