The director of the museum, Philippe de Montebello, described the bequest as "sensational" and "certainly the most important gift to the museum in the field of 20th-century art".
Mrs Gelman, who was born in what was then Bohemia, died last week at her home in Cuernavaca, Mexico, aged 86. Her husband, a Russian-born Frenchman who died 12 years ago, made a fortune producing films featuring the Mexican comedian Cantinflas. The value of their collection is estimated at more than $300m (pounds 188m).
Among the 85 works are an early self-portrait by Picasso that once belonged to Gertrude Stein, and Three Studies for a Self-Portrait by Francis Bacon, which will be the Museum's first examples of Bacon's painting. There is also one of the best-known Fauve portraits, Matisse's 1906 Young Sailor II.The Gelmans concentrated on the early 20th-century School of Paris. They had 14 Picassos, nine Matisses, nine Miros, four Braques, and single works by Renoir, Mondrian and Ernst. The earliest work is a Degas bronze sculpture from the turn of the century; the latest are the Bacons.
Mrs Gelman was an honorary trustee of the museum for many years, and promised it the collection in 1989 after the chairman of the 20th-century art department, William Lieberman, arranged for the works to go on public view for three months. There was generous tribute yesterday to Mr Lieberman, who had nurtured a friendship with Natasha Gelman ever since he organised a major Miro exhibition at the museum of Modern Art in the early Fifties. He advised the Gelmans on purchases, and when they endowed a curatorship of pre-Second World War art in 1990, he took the title.
In her will, Mrs Gelman stipulated that the collection should be kept together and not integrated into the museum's general collection.