Brabham was born in Hurstville, New South Wales, and became involved with cars and mechanics from childhood. He enlisted in the Royal Australian Air Force at 18 as a flight mechanic, working on Bristol Beaufighters. After his discharge in 1946 he started a small engineering workshop and was persuaded by an American friend to watch midget car racing — small open-wheel machines racing on dirt ovals that were hugely popular in Australia. He took over from his friend, and won on his third night of racing. Brabham went on to win the 1948, 1949, and 1950–51 Australian Speedcar Championships, earning the nickname "Black Jack" — variously attributed to his dark hair, his ruthless approach on track, and his reputation for maintaining a shadowy silence.
Brabham's interest shifted to road racing and he began buying and modifying Cooper cars from Britain. After competing in Australia and New Zealand, he moved to Europe in early 1955 and became embedded with the Cooper Car Company — working at the factory daily and contributing to the design of their mid-engined cars. His mid-engined Cooper approach was radical at a time when almost every racing car placed its engine at the front.
In 1959, Cooper obtained full 2.5-litre engines for the first time. Brabham won the Monaco Grand Prix after the leading cars ahead of him failed, then the British Grand Prix at Aintree, building a championship lead he would protect to the final race at Sebring. He ran out of fuel on the last lap while leading and pushed his car across the finish line to place fourth — enough to clinch the title. In 1960 he was more dominant, winning five consecutive Grands Prix. He pushed his car across the line yet again in 1957 at Monaco, this time to salvage sixth after racing for over three hours with a failed fuel pump mount.
In 1962, Brabham left Cooper to race his own cars, establishing the Brabham Racing Organisation with cars built by Motor Racing Developments — a company he had set up with fellow Australian Ron Tauranac. The early years under the new 1500cc formula were difficult; the team struggled with reliability and results, though Dan Gurney took the team's first championship win in 1964.
For 1966, a new 3-litre formula opened an opportunity. While other teams developed heavy, complex multi-cylinder engines, Brabham persuaded Australian engineering firm Repco to produce a new V8 based on an Oldsmobile aluminium block. The engine was not the most powerful, but it was lightweight and reliable. The combination of the Repco V8 and the Brabham BT19 proved decisive: Brabham won four consecutive Grands Prix and clinched his third title at the Italian Grand Prix. At the Dutch Grand Prix, irritated by press coverage of his age at 40, he arrived at the grid wearing a long false beard and leaning on a cane before winning the race. He became the only driver ever to win the Formula One World Championship in a car that carried his own name.
In 1967, Brabham's teammate Denny Hulme won the Drivers' Championship, while the team secured the Constructors' title. Brabham himself finished second.
In 1961, Brabham entered the Indianapolis 500 for the first time in a modified version of the Formula One Cooper with a 2.7-litre Climax engine, competing against Offenhauser-powered machines producing nearly twice the power. He qualified 17th and finished ninth. Though many American competitors dismissed rear-engined cars, his appearance at Indianapolis is credited with triggering a revolution: within five years, almost every car at the Brickyard was rear-engined.
In 1970, Brabham returned for one more season at the age of 44, and nearly won the Monaco Grand Prix on the final lap before locking his front wheels in a skid at the last corner and being overtaken by Jochen Rindt. He also ran out of fuel at the British Grand Prix while leading, handing Rindt another win. He retired after the Mexican Grand Prix, having tied Jackie Stewart for fifth in the championship standings. He was knighted in 1978 for services to motorsport — the first post-war racing driver to receive the honour.
After returning to Australia, Brabham pursued farming and business interests, including Engine Developments Ltd., a racing engine manufacturer established with John Judd in 1971. Three of his sons — Geoff, Gary, and David — all competed in motorsport, with Geoff winning five North American sportscar championships and the 24 Hours of Le Mans, and David also winning Le Mans. Brabham died at his home on the Gold Coast on 19 May 2014, aged 88, following a lengthy illness. He was the last surviving Formula One World Champion of the 1950s.