The USTA announced a news conference for Thursday to detail the plans, which are part of a major overhaul of the venue, including the creation of two new stadiums at New York's Billie Jean King National Tennis Center.
Despite frequent calls for a roof, last year the organisation ruled out including one as part of the redevelopment, citing logistical issues.
Center courts at Wimbledon and the Australian Open have retractable roofs, while the French Open has announced plans to cover its main court.
"For certain reasons it's great," Andy Murray, the reigning U.S. Open champion, told reporters after advancing to the third round of the Western and Southern Open in Cincinnati. "For TV and stuff, it's fantastic. Always good that you know matches are going to get finished.
"I don't necessarily miss being rained off but rain delays and stuff, it used to be part of it; whereas now that's kind of going away gradually.
"I don't particularly like going from indoors to outdoors to indoors but it's good for TV."
Opened in 1997, the Arthur Ashe stadium has a 22,500 capacity, making it by far the largest tennis stadium in the world but some, such as four-times U.S. Open champion John McEnroe, argued a smaller arena with a roof would have made more sense.
The scale of the arena has been one of the main logistical challenges that has emerged from previous feasibility studies with the USTA previously saying a roof would be "technically complex and financially challenging".
This year's U.S. Open, which starts on August 26, has a Monday finish included as the official final day for the first time.
But the switch to a scheduled Monday finish, unique among the four grand slam events, was criticised by the men's governing body the ATP.
(Reporting by Simon Evans in Miami, additional reporting by Steve Keating in Cincinnati. Editing by Ossian Shine and Frank Pingue)
