The Australian driver won the title in a car he built himself.
Motor racing legend Sir Jack Brabham won the championship in 1959, 1960 and 1966.
His son, David Brabham, confirmed that he had died at his home on Australia’s Gold Coast after a long battle with liver disease.
“He lived an incredible life, achieving more than anyone would ever dream of,” said David Brabham.
“He will continue to live on through the astounding legacy he leaves behind.”
Jack Brabham began racing in Australia in 1948 after serving in the Royal Australian Air Force as a mechanic.
After a number of successful years racing in New Zealand and Australia, he came to the UK and made his Grand Prix debut in 1955.
Jack Brabham’s Grand Prix wins ranged from his first in Monaco in 1959 to his last in South Africa in 1970, the year he retired from the sport.
His world championship win in 1966 was achieved in a car of his own construction, the rear-engined BT19.
He remains the only man in history to have designed, built and driven a championship-winning car.
Jack Brabham raced on into his 40s, recording his last of his 14 F1 victories at the age of 43 in the 1970 South African Grand Prix.
After his retirement, he sold his team to Bernie Ecclestone – who would go on to run the sport – with the Brabham name remaining in the sport until the 1990s.
Jack Brabham was knighted for services to motor sport in 1979. He is survived by his wife, Lady Margaret, and sons Geoff, Gary and David and their families.
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