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, which saw Cooke take the place of Terry Venables in the team. 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. 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.
In the early 1970s, Cooke was one of the star players in a flamboyant Chelsea side, alongside the likes of Peter Bonetti, Peter Osgood, Alan Hudson and Ian Hutchinson. They reached another FA Cup final, against Leeds United, in 1970. The first game ended 2–2 and, with Chelsea trailing 1–0 in the replay at Old Trafford with the clock running down, Cooke's run and chipped pass set up Osgood's equaliser with a diving header; Chelsea eventually won 2–1 after extra time. The Cup Winners' Cup was added in 1971 with a replayed win over Real Madrid in Athens. Chelsea reached a third consecutive cup final in 1972, this time the League Cup, and though Cooke again created the equaliser for Osgood, Chelsea lost to Stoke City.
He was sold to Crystal Palace shortly afterwards for £85,000 and made 44 appearances for the South London side, but returned to Chelsea a year later. 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-team mate Eddie McCreadie's young side earn promotion again in 1976–77. In his two spells at Chelsea, Cooke made 373 appearances, scoring 30 goals.
In 1980, he replaced his old Chelsea team mate, Eddie McCreadie, as the head coach of the Memphis Rogues. After new ownership moved the team to Calgary, Cooke himself moved to the California Surf where he played one last outdoor season. After this however, he continued to play in the indoor leagues, making his last appearance in the 1985–86 season for the Dallas Sidekicks.
He now runs a soccer school in Cincinnati, Ohio. In 2006, his autobiography The Bonnie Prince, written with Martin Knight, was published.