The US Track & Field organisation said Campbell, the decathlon gold medalist at the 1956 Summer Games, died at home in Gainesville, Georgia, on Friday.
Local news reports said he had suffered from cancer and diabetes.
"Campbell will forever be known as the first African American to win a gold medal in the decathlon and one of the greatest all-around male athletes in history," the organisation said.
Campbell, originally from New Jersey, also won the Olympic silver medal in the decathlon in 1952.
He excelled in other sports and spent time in both the National Football League and the Canadian Football League as a member of the Cleveland Browns and Montreal Alouettes.
Campbell was also an All-American swimmer in high school, national class in karate and named the world's greatest high school athlete in 1952.
A graduate of Indiana University, he was also a member of the Black Athletes' Hall of Fame and the US Olympic Hall of Fame.
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