Numerous reports from Havana said Stevenson died Monday of a heart attack.
Stevenson won the Olympic gold medal in the heavyweight class in 1972, 1976 and 1980. He was the first boxer to win three golds in the same weight class. In his 12 Olympic bouts, Stevenson had nine knockouts.
He missed a chance for a fourth gold medal when Cuba honored the Soviet Union's boycott of the 1984 Olympics in Los Angeles. He retired after the 1988 Games, which Cuba also boycotted.
Stevenson won world amateur championships in 1974 and 1978 as a heavyweight and 1986 as a super heavyweight. His all-time record is posted as 302-22.
He worked with the Cuban Boxing Federation and helped Cuba's Felix Savon to Olympic gold in the heavyweight class in 1992, 1996, 2000.
The only other boxer with three Olympic gold medals is Lazlo Papp of Hungary, who won the gold in 1948 as a middleweight and took first as a light middleweight in 1952 and 1956.