[2] Meyers accepted a basketball scholarship from the University of Washington and was soon recruited by Jim Owens to play football as well.

The athletics department created the John Meyers Defensive Player award in his honor for the basketball teams.

He was a captain of the 1960 Washington Huskies football team, which won a national championship.

On September 7, he was traded to the Dallas Cowboys along with linebacker Bob Long, in exchange for a third round draft choice (#32-Willie Brown).

On March 20, 1964, he was traded to the Philadelphia Eagles along with Sam Baker and offensive lineman Lynn Hoyem, in exchange for wide receiver Tommy McDonald.