(CNN) -- Australian motor racing legend Jack Brabham -- a three-time Formula One world champion and the only driver to win the title in a car bearing his name -- has died aged 88.

Over the course of a 15-year Formula One career beginning in 1955, Brabham won three drivers' world championships, becoming the first Australian to win the title despite coming late to the sport.

The first two titles, in 1959 and 1960, were earned as a driver for the Cooper team.

The third and most notable occurred in 1966, when, at 40-years-old, he won racing for Brabham, the successful car manufacturer and racing team he founded.

The team won the constructors' championships that season and the following year, with teammate Denny Hulme following in Brabham's footsteps to finish top of the drivers' standings in 1967.

"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," Brabham's youngest son, David, wrote in a message on the family's website.

David, who, like his two brothers, followed his father into a career in motorsport, said the racing legend had passed peacefully at his home on Australia's Gold Coast. He had eaten breakfast with his wife, Lady Margaret.

"It's a very sad day for all of us," said David, who spent two seasons in F1 in the 1990s but made a name for himself in sports cars, winning the 24 Hours of Le Mans in 2009.

Australian Prime Minister Tony Abbott declared that "Australia has lost a legend" as the news of his passing was announced. "With his pioneering spirit, Sir Jack Brabham personified many great Australian characteristics. He was respected and admired for his spirit and for his great skill as an engineer."

Late bloomer

The son of a Sydney greengrocer, Jack Brabham was an engineer by trade, working as a flight mechanic for the Royal Australian Air Force during the Second World War, as well as running a small engineering workshop.

He moved to Britain to pursue his racing career in the 1950s, and was eventually given his chance behind the wheel by Cooper in 1955, his appearance in the cockpit coinciding with the end of front-engined cars in the sport.

Four years later, he won the first of his three drivers' crowns, famously sealing his 1959 victory in the driver's championship by pushing his car to the finishing line after having run out of fuel on the last lap at the inaugural U.S. Grand Prix. He finished the race in fourth place to secure the title.

Brabham retired at the end of the 1970 season, the year of his 14th and final grand prix victory, selling his racing team at the same time.

In 1979, he became the first driver to be knighted for services to motorsport.

Brabham, the team he founded with Australian designer Ron Tauranac, won four Formula One drivers' championships and two constructors' championships during its three decades in operation.

Noted figures associated with the team included Hulme, Nelson Piquet, Bernie Ecclestone and McLaren chairman and CEO Ron Dennis.

'Most illustrious'

Dennis paid tribute to the man who gave him his first break in a statement on McLaren's website, calling him "one of the most illustrious names in motor racing history" and said Brabham's achievement in becoming Formula One champion in a car he built himself "will surely never be matched."

"The word 'legend' is often used to describe successful sportsmen, but often it exaggerates their status. In the case of Sir Jack Brabham, however, it's entirely justified," he wrote.

"When I started out in Formula One in the late 1960s, I worked first for Cooper and then for Brabham. Even as a callow youth, I could recognize greatness when I saw it, and I'll always regard it as an honor and a privilege to have worked for Sir Jack. I learned a lot from him too."

Mick Doohan, a five-time motorcycle world champion, said he was in awe of Brabham's achievements. "He set the bar pretty high," said Doohan. "He was a great guy and, looking back on what he achieved, it was just amazing."

Red Bull racer Daniel Ricciardo tweeted: "Sorry to hear about Sir Jack Brabham. A great Australian who inspired many Aussies to pursue our dreams."

Australian actor Eric Bana, himself a keen racer, also paid his respects. "Build them, race them, win them. We will never see another like the great Sir Jack Brabham," he tweeted.