The Briton, who won singles gold at the London Olympics in August, is the third seed thanks to the withdrawal of world number three Rafael Nadal through injury.
He is drawn in the same half of the draw as world number one Roger Federer - who beat him in straight sets in the 2008 final and in the final of Wimbledon this year - which means the two could theoretically meet in the semi-final.
Federer, who opens up against home hope Donald Young, is seeking to become the first man in 87 years to win the US Open six times.
Novak Djokovic, seeded second and defending champion at Flushing Meadows, will take on Paolo Lorenzi in the first round.
In the women's event, tournament favourite Serena Williams avoided most of her rivals as she was placed in the bottom half of the draw alongside second seed Agnieszka Radwanska.
The American fourth seed, who turns 31 next month and is coming off Wimbledon and Olympic triumphs, begins her title campaign against compatriot Coco Vandeweghe.
Defending women's champion Samantha Stosur of Australia, who beat Williams here last year for her first Grand Slam title, is in the top half together with world number one Victoria Azarenka and third seed Maria Sharapova.
"Winning here last year was an absolute dream come true. It's been a bit of an up and down year but I have been feeling good these past few weeks," said Stosur. "This is a tournament and a surface that I think suits my game, so hopefully I can have another great two weeks."
Women's top seed Azarenka, who won her first Grand Slam title at the Australian Open in January, opens against Alexandra Panova of Russia while Wimbledon runner-up Radwanska plays Russian Nina Bratchikova.
British hopes in the women's draw were handed tough rounds. Heather Watson opens against 2011 French Open winner Li Na, while Laura Robson could be matched against three-times US Open champion Kim Clijsters in the second round. In the bottom half of the draw Anne Keothavong is pitted against world number six Angelique Kerber.