Wilks, who hasn't worked in college football in 15 years, will replace Ryan Walters as Missouri's defensive coordinator.
Garrett was released from the Minnesota Vikings practice squad earlier this year.
Defensive coordinator will join Bret Bielema's Big Ten staff in the same capacity.
Cooper will have four years of eligibility remaining after spending one season at Ohio State.
Missouri's defense struggled mightily during its last three games of the 2020 season by giving up 148 points.