Bujones announced seven weeks ago he had lung cancer, but died Thursday of complications from melanoma, the Los Angeles Times reported Saturday.
Bujones reached the pinnacle of the ballet world in 1974, but Russian star Mikhail Baryshnikov defected at the same time granting instant U.S. stardom to the Russian, the Times said.
"Baryshnikov has the publicity, I have the talent," Bujones said at the time.
Born in Miami to Cuban parents, Bujones received early dance training in Havana. He went to the School of American Ballet in New York on a Ford Foundation scholarship and made his debut in 1970 with the Eglevsky Ballet.
He joined the American Ballet Theatre in 1972 and became its principal dancer after winning the gold medal in Bulgaria two years later. Bujones left ABT in 1985 and became a popular guest artist worldwide.
He danced at the White House for President Reagan in 1986 and became the first American to dance with the Bolshoi Ballet in Moscow in 1987, the same year he began an ongoing relationship with the Boston Ballet.
He returned to the ABT after Baryshnikov left in 1990, and remained a permanent guest artist until his farewell performance in 1995.
Survivors include his second wife, Maria; a daughter, his mother and father, one half brother and two half sisters.