"Van Cliburn was an international legend for over five decades, a great humanitarian and a brilliant musician whose light will continue to shine through his extraordinary legacy," Falcone said in a statement. "He will be missed by all who knew and admired him, and by countless people he never met."
Falcone had announced in late August that Cliburn had been diagnosed with advanced cancer and was being cared for at his home.
Cliburn skyrocketed to fame when he won the first International Tchaikovsky Competition in Moscow at age 23 in 1958, six months after the Soviets' launch of Sputnik embarrassed the U.S. and propelled the world into the space age. He triumphantly returned to a New York City ticker tape parade - the first ever for a classical musician - and a Time magazine cover proclaimed him "The Texan Who Conquered Russia."
The young man from the small east Texas town of Kilgore sold out concerts, caused riots when spotted in public and even prompted an Elvis Presley fan club to change its name to his. His recording of the Tchaikovsky Piano Concerto No. 1 with Russian conductor Kirill Kondrashin became the first classical album to reach platinum status.
The renowned pianist received multiple accolades, including the prestigious Kennedy Center Honors Medallion in 2001. He was presented with the Presidential Medal of Freedom by President George W. Bush in 2003, and then the next year, he was honored with the Order of Friendship of the Russian Federation from Russian President Vladimir Putin.
The Associated Press contributed to this report.
