Born in Barrie, Ontario, Storey was working in a rail yard when he received an offer to play football with the Toronto Argonauts. He was on the team for six seasons from 1936 to 1941, winning the Grey Cup in 1937 and 1938. During the 1938 Grey Cup game, Storey scored three touchdowns in twelve minutes versus Winnipeg, all in the fourth quarter, to give the Argos the victory. After his performance, he received offers from the New York Giants and the Chicago Bears of the National Football League but declined to leave Canada. He was forced to retire after suffering a knee injury.