Edmund, ranked 85th, opens play on court five against France's 13th seed Richard Gasquet at 16:00 BST.
Konta, seeded 13th, plays American Bethanie Mattek-Sands on the Grandstand court at around 00:00 on Tuesday.
Novak Djokovic, Rafael Nadal and Angelique Kerber also play on day one, while Andy Murray is among six Britons scheduled for day two.
The Scot, seeded second, will play Czech Lukas Rosol in the second night match at around 02:00 on Wednesday.
Heather Watson, Naomi Broady, Laura Robson, Dan Evans and Aljaz Bedene complete the British singles contingent.
Konta, 25, reached the fourth round last year but will face unfamiliar surroundings on Monday as she is among the first players scheduled to appear on the newly-constructed Grandstand arena.
The Briton will also face a newly crowned Olympic mixed doubles champion, with home support, in Mattek-Sands.
"She's playing inspired tennis," Konta told BBC Radio 5 live.
"She's coming off the back of winning gold in Rio and it's no secret that American players do rise to the occasion in the US. They love playing at home."
Edmund, 21, makes his debut in the US Open main draw and will take on former semi-finalist Gasquet for the first time.
