Williams died at his home in Los Angeles of complications from pancreatic cancer, according to his former publicist, Rob Wilcox.
Known as an electrifying stage performer and an adept improviser, Williams effortlessly switched between musical styles.
"Roger was one of the greatest pianists in the world and could play anything to classical music to jazz. He was one of the greatest personalities I've ever known," said Sen. Orrin Hatch of Utah, a longtime friend of Williams and himself a musician. "He could touch any audience, from teenagers to senior citizens."
Williams' 1955 hit "Autumn Leaves" was the only piano instrumental to reach number one on the Billboard pop charts. It remains the best-selling piano record of all time, with more than 2 million sold.
Nicknamed the "pianist to the presidents," Williams played for every commander in chief from Harry Truman to George H.W. Bush. His last trip to the White House was in 2008, when he performed at a luncheon for then-first lady Laura Bush.
Williams was good friends with Jimmy Carter, with whom he shared a birthday. When the two men turned 80, Williams played a 12-hour marathon at the Jimmy Carter Library and Museum in Atlanta, with the former president in attendance.
Born Louis Wertz in Nebraska, Williams started playing piano at age 3. By age 9 he was prolific with several instruments and could play anything by ear.
"I had a piano teacher growing up who would never play a song for me, she would make me play it from sheet music so I could learn to read music," Williams said, according to biographical information provided by Wilcox.
As a teenager, he was given his own 15-minute radio show on KRNT-AM, which was broadcast live from a Des Moines, Iowa, department store. Later he hosted a program on WHO-AM, where he first met the station's young sports announcer, Ronald "Dutch" Reagan. The two men started a friendship which lasted over 60 years.
Nancy Reagan said that when the two men met in Iowa all those years ago, "neither could have guessed that their careers would take them both to the White House someday."
The former first lady noted Saturday that in recent years Williams performed several times at the Reagan Library, including for a concert celebrating the late president's 100th birthday.
"Roger was a great pianist, a great American, and a great friend. I am saddened by his death, and my sympathy and prayers go out to his family," Nancy Reagan said in a statement.
Williams moved to New York to study jazz at the Juilliard School of Music. He won performing contests on the popular radio shows "Arthur Godfrey's Talent Scouts" and Dennis James' "Chance of a Lifetime."
Soon after, Williams was signed to Kapp Records, where founder Dave Kapp was determined to find a hit for the young prodigy. Producers decided on a shortened arrangement of "Autumn Leaves," which Williams recalled first clocked in at three minutes and three seconds.
"In those days the disc jockeys would not play a record over three minutes long. So Kapp asked if I could play the thirds a little faster. I did and it came in at two minutes and 59 seconds," Williams said, according to Wilcox.
It was an instant hit and catapulted Williams to national renown. He followed it up with a string of hits including "Born Free," "The Impossible Dream," "Theme From Somewhere In Time," and "Lara's Theme from Dr. Zhivago."
Williams became a popular guest on the top television shows of the time including "The Ed Sullivan Show," "The Perry Como Show," and "The Steve Allen Show."
In a 1995 interview with The Associated Press, Williams said he liked playing - and listening to - all types of music.
"The only thing I have against rock `n roll is the volume," he said.
He is the first pianist to be honored with on the Hollywood Walk of Fame, where his star was decorated with flowers Saturday. He also received the Lifetime Achievement Award from Steinway & Sons.
On his 75th birthday, Williams played a 12-hour marathon at Steinway Hall in New York City, a stunt he repeated several time in the following years.
In March, Williams announced on his website that he had been diagnosed with pancreatic cancer. A few days later he played his last concert, in Palm Desert, Calif.
Williams is survived by his daughters, Laura Fisher and Alice Jung, and five grandchildren.
Funeral services are pending.