Murray, who reached the number one ranking for the first time on Monday to end Novak Djokovic's 122-week reign, will begin his group round-robin matches on Monday against in-form Croatian Cilic.
Djokovic, whose form has dipped since he completed his career grand slam by winning the French Open for the first time in June, was placed in an easier-looking group with tournament debutants Gael Monfils and Dominic Thiem and Canada's Wimbledon runner-up Milos Raonic.
He has a combined 23-0 career record against that trio, leading Monfils 13-0, Raonic 7-0 and Thiem 3-0.
The 12-times grand slam-winning Serb will open on Sunday against world number nine Thiem.
Murray usurped Djokovic after winning the Paris Masters against John Isner on Sunday, although he was already assured of becoming the 26th player to top the ATP rankings when Raonic pulled out of their semi-final on Saturday.
Djokovic lost to Cilic in Paris at the quarter-final stage.
Murray has strung together 18 consecutive wins and has won his last four tournaments since losing in the US Open quarter-finals to Japan's Nishikori.
Cilic beat Murray in the Cincinnati final, shortly before the U.S. Open, while Swiss Wawrinka, the US Open champion, has beaten Murray seven times in 16 meetings, including at the Tour Finals last year when he won in straight sets.
