After playing at youth level for Port Glasgow and Renfrew Juniors,[3] Cooke began his professional career with Aberdeen in 1960, making his first team debut on 13 August in a 4–3 Scottish League Cup victory over Ayr United.

On his league debut the following season against West Ham United, Cooke waltzed past England's World Cup-winning captain Bobby Moore en route to scoring the winner for Chelsea.

He proved a versatile player when the post World Cup tactics limited the use of wingers and he was often played in a deeper right midfield position behind Tommy Baldwin who had replaced George Graham in a direct swap between Chelsea and Arsenal.

By that stage, the club were in decline and were relegated in 1974–75, though Cooke's experience proved invaluable in helping manager and ex-teammate Eddie McCreadie's young side earn promotion again in 1976–77.

Cooke left Chelsea for the second and final time in July 1978 to play for numerous American teams, including the Memphis Rogues, Los Angeles Aztecs and California Surf in the now-defunct NASL.