“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 Grand Prix Corporation said Brabham died after a long illness.
“He had a long battle with liver disease,” an AGPC official told AFP.
The Australian was a major influence in the world of Formula One, winning three drivers’ championships, in 1959 and 1960 with the Cooper Racing Team and again in 1966 in his own Brabham car.
His first two titles in the Cooper Climax marked the end for front-engined Formula 1 cars.
In 1959 he famously ran out of fuel at the United States Grand Prix and pushed his Cooper Climax across the finish line to end fourth and become Australia’s first Formula 1 world champion.
Brabham, a former Royal Australian Air Force mechanic, in later years recounted the amazing tale.
“My car ran out of petrol about half a mile from the end. I couldn’t do anything but just coast to a stop,” he told the Australian Broadcasting Corporation.
“I eventually stopped about 100 yards from the finishing line, and I started pushing. If anybody assisted me, I’d be disqualified.
“It was a big thrill to me to find out after I was exhausted on the ground, I found out that I’d actually won the championship. It was a fantastic thing.”
Seven years later he became the only driver to win the world championship in a car bearing his own name, the Brabham BT19 Repco in 1966. He also won the constructors’ championship that year, and again in 1967.
Brabham started in 126 Grand Prix from 1955 to 1970, amassing 14 wins, 31 podiums, 13 pole positions and 12 fastest laps.
Acclaimed as a brilliant engineer, technological innovations brought about by the team he created helped shape the sport.
Through his partnership with Ron Tauranac, more than 500 Brabham race cars were built from the team’s British Surrey base in the 1960s alone, while the Brabham name continued in Formula One for 30 years.
He claimed his final Formula One win in the 1970 South African Grand Prix before retiring that year.
Briton Stirling Moss, one of his fiercest rivals, told the ABC in 2009 that Brabham was always held in the highest esteem in racing circles.
“Sir Jack was the first Australian to come over and really make a mark. I mean, he is after all, he is one of the best known Australians in the world,” he said.
“I mean, you’ve got Don Bradman and a few other guys, but very few people in the world have achieved what he’s achieved in his sport.”
Brabham was awarded the Order of the British Empire in 1967 and became the first driver to be knighted for services to motorsport in 1979.
In his final years, he battled failing eyesight and problems with his kidneys and liver.
He passed away at his home on Australia’s Gold Coast just a day after making his last public appearance at a local airport at Queensland state’s Sunshine Coast, where he was reunited with the 1967 BT23 race car he designed and built.