Hulme was born on a tobacco farm in Motueka in the South Island of New Zealand. His father, Clive Hulme, was awarded the Victoria Cross for his actions as a sniper during the Battle of Crete in 1941. Growing up on the family farm near Pongakawa, Denny learned to drive a truck as a child and later left school to work in a garage. He purchased an MG TF and entered hillclimbing events, then progressed to a Formula 2 Cooper-Climax. He was selected for the New Zealand Driver to Europe programme, alongside George Lawton, and competed in Formula Junior and Formula Two across Europe from 1960.
After winning the 1961 New Zealand Gold Star Championship in a car hired from Reg Parnell, Hulme came to the attention of Jack Brabham. He worked as a mechanic in Brabham's Chessington garage while developing his racing career. Brabham gave him drives in sportscars and single-seaters, and after several seasons in Formula Two — during which the pair dominated the FFSA Trophées de France series — Hulme was invited to join the Brabham Formula One team.
Hulme made his World Championship debut at the 1965 Monaco Grand Prix. In 1966, his first full season, he finished fourth overall with four podium finishes. The 1967 season brought the title in a closely fought campaign against his own team leader Jack Brabham and the fast-closing Lotuses of Jim Clark and Graham Hill. Hulme won at Monaco and at the Nürburgring — the latter victory on the fearsome Nordschleife demonstrating his versatility across all track types. He took the title by five points from Brabham and ten from Clark, becoming the first New Zealander to win the Formula One World Championship.
Hulme moved to the McLaren team for 1968, joining fellow New Zealander Bruce McLaren. Early in the season he suffered burns to his hands during a methanol fire at practice for the Indianapolis 500, causing him to miss the Dutch Grand Prix. Despite these setbacks he took two wins that year, at Monza and in Canada, finishing third in the championship. He won the 1969 Mexican Grand Prix in the season's final round.
The death of Bruce McLaren during testing in 1970 was a profound blow. Hulme finished fourth in the championship that year despite his emotional distress and ongoing recovery from his hand injuries. A revival came in 1972, partnered with Peter Revson, when Hulme won in South Africa and achieved a string of podiums to finish third in the championship. He won the 1973 Swedish Grand Prix after both Ronnie Peterson and Emerson Fittipaldi encountered late trouble, and the following year took victory in the Argentine Grand Prix. The death of Revson during testing at Kyalami in 1974 deepened Hulme's growing apprehensions about the dangers of racing. He retired from Formula One at the end of that season, having scored eight Grand Prix victories, one pole position, nine fastest laps, and 33 podiums across his career.
Hulme's record in the Canadian-American Challenge Cup is among the most impressive in sports car history. After modest beginnings in the 1966 inaugural season, he joined the McLaren team the following year and formed what American observers called the "Bruce and Denny Show." He won the Can-Am Championship in 1968 and 1970 and was runner-up four times in the series from 1967 to 1972. His 22 career Can-Am victories remain the all-time series record. He won six of ten races in 1970 alone to lead the McLaren team through its difficult first season without Bruce McLaren.
Hulme competed at Indianapolis four times — 1967, 1968, 1969, and 1971 — with his best results being fourth place in both 1967 and 1968. He was named the 1967 Indianapolis 500 Rookie of the Year.
On 4 October 1992, while competing in the Bathurst 1000 at Mount Panorama, Hulme suffered a massive heart attack at the wheel on the high-speed Conrod Straight. He brought the car to a controlled stop against the safety railing and was taken to Bathurst Hospital, where he was pronounced dead. He was 56 years old. His sister later suggested his health had declined significantly following the death of his son Martin on Christmas Day 1988.
Hulme was appointed an Officer of the Order of the British Empire in 1992, inducted into the New Zealand Sports Hall of Fame in 1993, and into the International Motorsports Hall of Fame in 2002. The Denny Hulme Memorial Trophy is awarded at the Targa Tasmania, and a NZ Motor Cup trophy in his name is presented during the Toyota Racing Series. He was portrayed by Ben Collins in the 2019 film Ford v Ferrari.