Brabham was born on 2 April 1926 in Hurstville, New South Wales. He was involved with cars and mechanics from childhood, learning to drive the family vehicles at age 12. He left school at 15 to work at a garage while taking evening mechanical engineering classes. At 18 he enlisted in the Royal Australian Air Force as a flight mechanic, maintaining Bristol Beaufighters at RAAF Station Williamtown. He was discharged on his 20th birthday and immediately started a service and repair workshop.
An American friend introduced him to midget car racing, and Brabham quickly discovered his aptitude for the sport, winning on his third night's racing. He won the Australian Speedcar Championship in 1948, and the Australian and South Australian championships in 1949. He won further Australian championships in 1950 and 1951, earning the nickname "Black Jack" — attributed variously to his dark hair and stubble, his ruthless track approach, and his "shadowy silence." He moved into road racing in 1953, winning the Queensland Road Racing championship, and was persuaded after the 1954 New Zealand Grand Prix to try racing in Europe.
Arriving in Europe alone in early 1955, Brabham integrated himself into the Cooper Car Company, initially without a formal arrangement, working daily at their factory from mid-season. He made his Grand Prix debut at the 1955 British Grand Prix in a Cooper Bobtail, and demonstrated his worth against Stirling Moss in a non-championship race at Snetterton that year.
Brabham contributed to the development of Cooper's mid-engined design and was central to the team's success as rear-engined layouts became dominant. In 1959, after Cooper finally obtained full 2.5-litre engines, Brabham won the Monaco Grand Prix and the British Grand Prix, eventually clinching the championship at the United States Grand Prix at Sebring after running out of fuel on the final lap and pushing his car to fourth place. He won the title by four points from Tony Brooks.
In 1960, he won five consecutive Grands Prix — Dutch, French, Belgian, British, and Portuguese — to retain the championship comfortably. His expertise in setting up the cars was cited as a significant factor in Cooper's consecutive Drivers' and Constructors' titles. The Cooper was noted for its mid-engined layout, which Brabham and his car took to the Indianapolis 500 in 1961, qualifying 17th and finishing ninth. Although the car was slower on the straights, its superior handling in corners demonstrated the viability of rear-engined cars at the Speedway and "triggered the rear-engined revolution at Indy" — within five years nearly all Indianapolis competitors used the layout.
Dissatisfied with Cooper's unwillingness to develop faster cars, Brabham left after 1961 to race for his own team. With fellow Australian Ron Tauranac, he founded Motor Racing Developments (MRD) and the Brabham Racing Organisation. The 1500cc formula introduced in 1961 did not suit the team, and Brabham went without a win until a new 3-litre formula took effect in 1966.
For 1966, Brabham identified an aluminium Oldsmobile F-85 engine block and persuaded Australian engineering company Repco to develop a new 3-litre V8 around it. The combination prioritised light weight and reliability over outright power. At the French Grand Prix at Reims-Gueux, Brabham won for the first time since 1960 and became the first man to win a Formula One World Championship race in a car of his own construction. He won three more races that season and clinched the championship at the Italian Grand Prix, becoming the only driver to win the Formula One World Championship in a car bearing his own name. In a characteristically uncharacteristic stunt, he had appeared on the starting grid at the Dutch Grand Prix that year wearing a false beard and leaning on a cane in response to press stories about his age — then went on to win the race.
In 1967, teammate Denny Hulme won the championship while driving for Brabham's team. The constructor went on to win two further Drivers' Championships in the 1980s under Bernie Ecclestone's ownership.
Brabham suffered serious foot injuries in a 1969 testing accident but returned before the season's end. Planning to retire, he instead raced one final season in 1970 and nearly won the Monaco Grand Prix, holding the lead into the final corner of the final lap before locking his front wheels and sliding wide, losing to Jochen Rindt. He also lost the British Grand Prix at Brands Hatch while leading when he ran out of fuel at the final corner. He retired after the Mexican Grand Prix in 1970, aged 44. His final top-level race win came at the Paris 1000 km in October 1970, driving for the Matra sportscar team.
Brabham was the first post-war racing driver to be knighted, receiving the honour in 1978. He was inducted into the International Motorsports Hall of Fame in 1990. The suburb of Brabham in Perth, Western Australia, is named in his honour. Three of his sons — Geoff, Gary, and David — became professional racing drivers; Geoff won the 24 Hours of Le Mans and five North American sportscar championships. Brabham was the last surviving Formula One World Champion of the 1950s era. He died at his home on the Gold Coast on 19 May 2014, aged 88, following a lengthy battle with liver disease.