"The Cuban sporting family was moved today by the passing of one of the greatest of all time," said a statement read on the news Monday night in Havana. Stevenson died of heart disease, it added.
Considered by some to be the most accomplished amateur boxer in history, Stevenson first won gold in 1972 in Munich and followed that up in 1976 in Montreal.
In 1980, he won his third Olympic title in Moscow, becoming the second boxer to win gold at three separate Games after Hungarian Lazlo Papp. Felix Savon, Stevenson's countryman, accomplished the feat in 2000.
The 6-foot-31/2-inch Stevenson was famous for his punishing right, polished technique, deft hand and footwork, and sportsmanship.
Stevenson was born in 1952 to a Jamaican family of modest means and grew up in Las Tunas province in eastern Cuba, where his parents were farm laborers. He fought in his first match at the age of 14, and two years later won his first international title in the Central American and Caribbean championship.
As his accomplishments grew, boxing fans began salivating over the prospect of a "fight of the century" pitting him against Muhammad Ali. But Cuba insisted he not lose his amateur status, and the bout never took place.
After Stevenson won his first world title in 1974, Sports Illustrated ran the headline: "He'd Rather Be Red Than Rich."
Stevenson won world amateur titles again in 1978 and 1986. He was forced to pass up a shot at a fourth Olympic gold when Cuba did not attend the 1984 Games in Los Angeles. He retired in 1988 after Cuba decided to skip the Seoul Olympics as well.
Stevenson passed up millions by not leaving Communist-run Cuba to turn pro, but expressed no remorse.
"I prefer the affection of 8 million Cubans," he once said.
In his later years, Stevenson served as vice president of Cuba's boxing federation and at the island's national sports institute. He had two children.