Olympic champion Andy Murray will meet Czech Lukas Rosol in the first round of the US Open, which starts on Monday.
The British second seed, 29, beat world number 82 Rosol 4-6 6-3 6-2 in a heated match at the Munich Open last year.
British number two Dan Evans faces American Rajeev Ram, while Kyle Edmund will play France's Richard Gasquet.
Briton Johanna Konta, seeded a career-high 13th in the women's singles, meets American Bethanie Mattek-Sands, who won mixed double gold at the Rio Olympics.
Top seed and world number one Novak Djokovic begins the defence of his men's title against world number 120 Jerzy Janowicz, while Spaniard Rafael Nadal, the 2010 and 2013 champion, meets Denis Istomin of Uzbekistan.