Hulme was born on a tobacco farm in Motueka, South Island. 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 Te Puke, Denny learned to drive a truck on his father's lap; by age six he was driving solo. After leaving school and working in a garage, he saved enough to buy an MG TF and began hillclimbing. He was subsequently selected for the New Zealand Driver to Europe programme, competing in Formula Junior and Formula Two alongside fellow New Zealander George Lawton. The year 1960 ended in tragedy when Lawton died in Hulme's arms after a crash at Roskilde, Denmark.
Hulme established himself in Europe by basing himself in London, working as a mechanic in Jack Brabham's Chessington garage while racing in Brabham sportscars and single-seaters. He won seven international Formula Junior races in 1963 and the FFSA Trophées de France Formula Two title twice alongside Brabham. His development as a driver was gradual and unglamorous, built on consistency and technical sensitivity rather than overnight stardom.
Hulme made his World Championship debut at Monaco in 1965 as a Brabham works driver, scoring his first points later that year. In 1966 he completed his first full season, finishing fourth overall while Brabham took the drivers' title.
The 1967 season brought Hulme the championship. Sharing the team with Brabham, he won at Monaco and on the Nürburgring Nordschleife, six more podiums rounding out a consistent campaign. He beat Brabham by five points and Jim Clark by ten to take the title — despite the Brabham-Repco being neither the fastest nor the most powerful car in the field. It was a championship won by reliability and racecraft.
For 1968 Hulme moved to the McLaren team, where he would spend the rest of his Formula One career. He added race victories at Monza and in Canada that year, finishing third overall. After a difficult 1969, he suffered burns to his hands during a methanol fire at the 1970 Indianapolis 500 practice, missing one Grand Prix. His friend and team boss Bruce McLaren was killed that year while testing in England, a loss that affected Hulme deeply. He nonetheless continued racing, finishing fourth in the championship.
Hulme enjoyed a revival in 1972, winning in South Africa alongside team-mate Peter Revson and finishing third in the championship. In 1973 he won the Swedish Grand Prix after the leading Lotuses encountered problems late in the race, though he noted sadness at denying Ronnie Peterson a home victory. He recorded only a single career pole position, at the 1973 South African Grand Prix. He announced his retirement from Formula One following the death of Revson in testing at Kyalami in March 1974, seeing out the season and taking one final victory in Argentina before stepping away from the sport.
Hulme's record in the Canadian-American Challenge Cup was arguably more dominant than his Formula One achievements. After an uncompetitive debut season in 1966, he joined the McLaren team in 1967 and the "Bruce and Denny Show" became the most feared pairing in the series. He won the Can-Am Drivers' Championship in 1968 and again in 1970, after McLaren's death, leading the team through bereavement to six wins in ten races. Across six seasons from 1967 to 1972 he was champion twice and runner-up four times, and his 22 career wins remain the most by any driver in series history.
Hulme contested the Indianapolis 500 four times: 1967, 1968, 1969, and 1971. He finished fourth in both 1967 and 1968, and was named 1967 Indianapolis 500 Rookie of the Year. A methanol fire during 1970 practice forced his withdrawal that year.
After retiring from Formula One Hulme returned to New Zealand and to touring car racing, periodically competing in Australian events. He raced in European Touring Cars in 1986, winning a fourth RAC Tourist Trophy, and drove for several Australian teams into the early 1990s. During the 1992 Bathurst 1000, while driving a BMW M3 on the high-speed Conrod Straight, Hulme suffered a massive heart attack at the wheel. He managed to bring the car to a controlled stop against the safety railing before marshals reached him, but he was pronounced dead at Bathurst Hospital.
Hulme was inducted into the Motorsports Hall of Fame of America in 1998 and the International Motorsports Hall of Fame in 2002. New Zealand named the Denny Hulme Memorial Trophy, awarded at the Targa Tasmania, in his honour. He was appointed an Officer of the Order of the British Empire in 1992. He remains the only Formula One World Champion from New Zealand.