Brabham won three world drivers' championships and remains the only man to win one in a car he built himself. He was also the first driver to be knighted for services to motorsport.
"It's a very sad day for all of us. My father passed away peacefully at home at the age of 88 this morning," son David Brabham said in a statement.
"He lived an incredible life, achieving more than anyone would ever dream of and he will continue to live on through the astounding legacy he leaves behind."
The Australian won drivers' championships in 1959 and 1960 with the Cooper Racing Team and again in 1966 in his own Brabham car.
The motorsport world mourned his passing with fellow Australian Formula One champion Alan Jones hailing him as "inspirational".
"I think he was inspirational for any young bloke that wanted to go across overseas and race cars," said Jones, who won the world championship in 1980.
"He was the man they looked up to and he was the man they wanted to emulate."
The Confederation of Australian Motorsport (CAMS) revered the F1 trailblazer, known as "Black Jack."
"Always a man of few words -- his nickname 'Black Jack' referred to both his dark hair and his propensity for maintaining a shadowy silence -- he avoided small talk and was undemonstrative in the extreme," a statement on the CAMS website said.
"But behind the wheel he was anything but shy and retiring. He put his head down and drove exceedingly forcefully."
Brabham's first two titles in the Cooper Climax marked the end of the era of front-engined Formula 1 cars.
In 1959 he famously ran out of fuel at the United States Grand Prix and pushed his car across the finish line to take fourth place and become Australia's first Formula 1 world champion.
Brabham, a former Royal Australian Air Force mechanic, in later years recounted the amazing tale.


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