Manager Jean Pierre Leduc says Jones died Sunday night at a hospital in New York after a brief illness.
Jones won a Grammy lifetime achievement award last year and received the National Medal of Arts in 2008. He also worked as an accompanist to Ella Fitzgerald.
He continued to perform until the end. He was scheduled to play at the landmark Birdland Jazz Club in New York City next week.
At last year's Jazz Awards, Jones was voted pianist of the year. The crowded field of nominees included such distinguished veterans as Kenny Barron and Keith Jarrett.