Mary Lou Falcone, the musician's spokeswoman and longtime friend, confirmed his death to The Washington Post.
Among his accomplishments were winning the gold medal in Moscow's Tchaikovsky International Piano Competition in 1958. When he returned home, he was treated to a New York ticker-tape parade and was regarded as an American hero for years.
Although he retired in 1978 from regularly performing, he could be coaxed into taking the bench for some special events and benefits, the Post said.
"I do play concerts from time to time," he told the New York Times in 2008. "I work at home quietly, go to the opera, hear concerts, see friends. I like making up now for what I was not able to have then."
Van Cliburn was recognized at the Kennedy Center Honors in 2001. President Barack Obama presented him with the National Medal of Arts at the White House in 2010.
"Since his historic 1958 victory at the first International Tchaikovsky Competition in Moscow, Mr. Cliburn has reached across political frontiers with the universal message of beautiful music," Obama said.