"It is a forum for young artists to celebrate the great works of the piano literature and an opportunity to expose their talents to a wide-ranging international audience," Cliburn said during the 10th competition in 1997.
The 14th competition is to be held in May and June and will be dedicated to Cliburn's memory.
Cliburn's "Rachmaninov: Piano Concerto No. 3" won a Grammy for best classical performance in 1959, and he was awarded the Grammy Lifetime Achievement Award in 2004.
The Recording Academy, which bestows the awards, said Wednesday that Cliburn transcended cultural barriers and politics through the power of his music, and "his legacy will continue to have a great impact not only on classical music, but on our culture as well."
In 2003, President George W. Bush presented Cliburn with the Presidential Medal of Freedom — the nation's highest civilian honor. The next year, he also received the Order of Friendship of the Russian Federation from Russian President Vladimir Putin.
"I still have lots of friends in Russia," Cliburn said at the time. "It's always a great pleasure to talk to older people in Russia, to hear their anecdotes."
After the death of his father in 1974, Cliburn announced he would soon retire to spend more time with his ailing mother. He stopped touring in 1978.
He told The New York Times in 2008 that among other things, touring robbed him of the chance to enjoy opera and other musical performances. "I said to myself, 'Life is too short.' I was missing so much," he said. After winning the competition, he added, "it was thrilling to be wanted. But it was pressure too."