Jeanne-Claude died Wednesday night at a New York hospital from complications of a brain aneurysm, her family said in an e-mail statement.
Mayor Michael Bloomberg said he spoke with Christo on Thursday morning and offered condolences on behalf of all New Yorkers.
"The Gates" festooned 23 miles of Central Park's footpaths with thousands of saffron drapes hung from specially designed frames.
More than 5 million people saw "The Gates," and it was credited with injecting about $254 million into the local economy.
Christo the more famous of the duo was saddened, the family statement said, but remains "committed to honor the promise they made to each other many years ago: that the art of Christo and Jeanne-Claude would continue." That includes completing their current installation, "Over The River, Project for the Arkansas River, State of Colorado" and "The Mastaba" a project in the United Arab Emirates.
The Colorado project which they had done parts of on and off for decades involves spanning miles of the river with woven fabric. They chose the location near Canon City because of its river rapids and access to roads and footpaths. It is expected to be realized by the summer of 2013, at the earliest, according to the statement, which was issued from the couple's home office.
Their other projects include wrapping the Reichstag in Germany, the Kunsthalle in Bern, Switzerland, a Roman wall in Italy, and the Pont Neuf in Paris.
A 1991 project involved thousands of bright yellow and blue umbrellas positioned across miles of inland valleys in Japan and California.
Their projects required mammoth manpower and miles of fabric and other materials. For the umbrella project, a total of 1,880 workers were used. They recycled all materials following each project.
The couple said they never accepted any sponsorship and financed all their temporary installations through the projects, including the sale of their preparatory drawings, collages, scale models and original lithographs.
The Mastaba (the Arabic word for bench) envisions a pyramid-like structure made of 410,000 brightly colored oil barrels stacked horizontally and rising 492 feet high and 984 feet wide.
"Hundreds of bright colors, as enchanting as Islamic mosaics, will give a constantly changing visual experience according to the time of the day and the quality of the light," the artists' Web site says of the project.
The couple was looking at five possible sites for the project at the time of Jeanne-Claude's death, the statement said.
The two artists met in Paris in 1958 and had been collaborating for 51 years on temporary public arts projects. They made their home in Manhattan, where they had lived for 45 years.
Jeanne-Claude, who sported signature orange-dyed hair, once said that the couple, like parents who wouldn't favor one child over another, felt that, "each project is a child of ours."
But she added that their favorite project was, "the next one."
Plans for a memorial will be announced at a later date, but the family said they will donate her body to science, as was her wish.