Bruce's family announced his death via Facebook and the musician's official website.
"It is with great sadness that we, Jack's family, announce the passing of our beloved Jack: husband, father, granddad and all-round legend," the statement said. "The world of music will be a poorer place without him, but he lives on in his music and forever in our hearts."
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No further details were provided, but the Press Association reported that Bruce died of liver disease.
Bruce is best known as a member of the 1960s British band, Cream, performing alongside members Eric Clapton and Ginger Baker. Formed in 1966, Cream went on to sell 35 million albums in just two years, according to Bruce's website. The band's third album, Wheels of Fire became the first-ever platinum-selling double album. Cream split shortly after its debut in 1968, and Bruce went on to front his own bands.
"Jack felt that he had strayed too far from his ideals, and wanted to re-discover his musical and social roots," according to Bruce's website.
He returned to the studio to record his 2001 solo album Shadows in the Air, which hit no. 5 on the British jazz and blues chart.
Bruce was born to musical parents in Glasgow, Scotland, on May 14, 1943. His parents traveled extensively in Canada and the U.S., and a young Bruce attended 14 different schools. He finished his formal education at Bellahouston Academy and the Royal Scottish Academy of Music, to which he won a scholarship for cello and composition.
Bruce left Scotland at 16, and in 1962, joined his first important band, the influential Alexis Korner's Blues Inc., in London. It featured drummer Charlie Watts, who later joined The Rolling Stones.