Williams died following a long bout with pancreatic cancer, his assistant, Jacque Heeber, told CNN. She said Williams was still performing, had recently released an album and was contracted to record three more.
"There was never a man with a more tender, gentle heart," she said.
Williams, who performed for nine U.S. presidents and was an advocate for music education, was born Louis Weertz in Omaha. He attended Drake University and the Juilliard School in New York.
His association with Dave Kapp, the founder of Kapp Records, helped springboard him to stardom. It was Kapp who suggested the pianist record "Autumn Leaves" -- and Kapp who suggested he change his name, the Los Angeles Times said.
Williams' 1955 recording of "Autumn Leaves" began a streak of four decades in which Williams charted on Billboard, his official Web site said.
"I owed two months' rent on our apartment," Williams told the Times in 1996. "I had a wife and a baby at the time. My fondest dream for 'Autumn Leaves' was that it would pay the rent. And boy, it's been doing it ever since."
Former U.S. first lady Nancy Reagan issued a statement calling Williams "a great pianist, a great American and a great friend" She said Williams had been friends with former President Ronald Reagan for decades and had performed many times at the Reagan Library in Simi Valley, Calif.