Cook was promoted to general manager of the New York Yankees on June 30, 1981 after Bill Bergesch was hired by Bob Howsam to be GM of the Cincinnati Reds.

Murray Cook earned Steinbrenner's wrath when the Oakland Athletics selected pitcher Tim Belcher from the Yankees in the free agent compensation draft on February 8, 1984.

Cook inherited the title of vice-president and director of scouting in the shuffle, as Steinbrenner stated that "I take the blame of asking a young man to move too fast too soon".

His first action after taking over was to hire Buck Rodgers, who had just won the Minor League Manager of the Year Award by leading the Expos' AAA farm team, the Indianapolis Indians to a 91-63 record and the American Association championship.

On August 11, 1987, the Expos called a hasty press conference to announce Cook had been fired and Vice-President for Baseball Administration Bill Stoneman was taking over as general manager.

On Saturday June 21, 2014, Cook was inducted into the Canadian Baseball Hall of Fame, in St. Marys, Ontario, along with former Montreal Expos announcer Dave Van Horne and their popular long time slugging third baseman Tim Wallach.