The move will bring the US Open into line with Wimbledon and the Australian Open which both have retractable roofs on their centre courts. The French Open has announced plans to cover its main court.
Two new stadiums will be also be added as part of a £350 million overhaul of the Billie Jean King National Tennis Center in Flushing Meadows, New York, a project which should be completed by 2018.
The huge Arthur Ashe Stadium - by far the biggest in tennis - was always assumed to be unroofable, given the sheer size of the structure.
But the new roofs in question get around the problem by use of revolutionary new materials: they will not be made not from glass, plastic or fibreglass, but from fabric.
In other words, the USTA is building a giant umbrella that can be hauled over the stadium. The roof for the Arthur Ashe Stadium alone will cost £70 million.
"In order to have spectacular facilities we want to make sure we have the excitement and the energy that New York deserves and the world comes to see," Dave Haggerty, the USTA's chairman of the board, said.
"Our strategic mission, when completed, will have a couple of new stadiums, a better fan experience, we will have wider walkways so that people can get around and, yes, as you have heard, there will be a roof on Arthur Ashe Stadium.
"In addition Louis Armstrong (Stadium) will have a roof as well."
The Arthur Ashe Stadium roof will be made of teflon-coated fabric that is translucent in appearance and will be stretched over a colossal steel frame in four panels, each weighing around 400 tonnes.
Eight new steel columns will be built around the huge stadium to support the weight of the roof, which can be opened or shut in as little as seven minutes.
It will measure 200,000 square feet and organisers hope to have it installed "at the earliest for the 2016 US Open and most likely by the 2017 US Open".
A new 8,000-seat Grandstand Stadium court will be constructed in time for 2015 followed by a 15,000-seat Louis Armstrong Stadium court to be opened before the 2018 edition.
"We recognise there are many known, and certainly many unknown, hurdles we will have to confront to meet this schedule," said USTA executive director Gordon Smith. "We are ready for the challenge and hope we can achieve it."
Andy Murray, the US Open champion who is competing this week at the Western and Southern Open in Cincinnati, welcomed the news.
"For TV and stuff it's fantastic," he said. "Always good that you know matches are going to get finished ... 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."
Bad weather has wrought havoc with the US Open schedule in recent years with the men's final, including last year's epic between Murray and Novak Djokovic, being pushed back from Sunday to Monday for the past five years.
Despite frequent calls for a roof, the USTA last year ruled out including one as part of the redevelopment, citing logistical issues.
Opened in 1997, Arthur Ashe Stadium has a 22,500 capacity, making it by far the largest tennis arena in the world but some, such as four-times US Open champion John McEnroe, argued a smaller venue 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 feasibility studies with the USTA previously saying a roof would be "technically complex and financially challenging".
This year's US Open, which starts on August 26, has a Monday finish included as the official final day for the first time.
The switch to a scheduled Monday finish, unique among the four grand slam events, has been criticised by the men's governing body, the ATP.