Cooke began his professional career with Aberdeen in 1960 and moved to Dundee in December 1964, where he was voted player of the year. He signed for Chelsea in April 1966 for a then club record of £72,000 as part of manager Tommy Docherty's restructuring of the Chelsea side. He made his debut in May 1966 during a 2–0 Inter-Cities Fairs Cup win over FC Barcelona. 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. Cooke took the place of Bert Murray on the right wing as several players were replaced owing to a growing rift between Docherty and his players. 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. His debut season saw Chelsea reach the FA Cup final against Tottenham Hotspur (Cooke's cross had created Tony Hateley's winner for Chelsea in the semi-final against Leeds United). Cooke had a shot tipped over the bar by Pat Jennings early on, but Chelsea generally underperformed and lost 2–1.