Cliburn, whose triumph at the Moscow competition, made him an international celebrity died on Wednesday after battling bone cancer. He was 78.
Obama said he had heard Cliburn play and was touched by his talent.
“Like every President since Harry Truman, I enjoyed the privilege of hearing Mr. Cliburn play, and I am confident that the enduring beauty of his art will sustain his legendary status for years to come,” said the president.
Cliburn was honored in 2003 by President George W. Bush, who presented him with the Presidential Medal of Freedom and in 2010 when Obama awarded him the National Medal of Arts.