Redman began racing in 1959 and graduated to international competition by the mid-1960s. His first Manufacturers Championship came in 1968 driving a Ford GT40 with Jacky Ickx for John Wyer Automotive Engineering. That same year he also drove a Gulf-sponsored Wyer prototype and began what became a long and successful association with the world's leading sports car programmes.
As a Porsche works driver in 1969 and 1970, and then with Ferrari's 312 PB in 1972, Redman accumulated victories at the sport's most demanding circuits. His record includes wins at Spa-Francorchamps more than once, four triumphs at the Nürburgring 1000 Kilometres, two victories each at the 24 Hours of Daytona, the 12 Hours of Sebring, the Watkins Glen 6 Hours, Brands Hatch 6 Hours, the Österreichring 1000 Kilometres, and the Monza 1000 Kilometres. He also won the 1970 Targa Florio and the Kyalami 9 Hours twice, and holds two class victories at the 24 Hours of Le Mans. He additionally won the 1970–71 South African Springbok series.
Redman participated in fifteen World Championship Grands Prix, making his debut on 1 January 1968. He achieved his sole podium at the 1968 Spanish Grand Prix, finishing third in a Cooper-BRM behind Graham Hill and Denny Hulme. That year he also suffered a serious accident at the Belgian Grand Prix at Spa-Francorchamps when the suspension of his Cooper-BRM broke at Les Coombes corner; he survived with a badly broken arm. He scored eight championship points in total, including two fifth-place finishes in 1972 at Monaco and the German Grand Prix driving a Yardley McLaren. He also raced in Formula One for Shadow and Williams.
In 1973 Redman relocated to the United States to race full-time. From 1974 to 1976 he won three consecutive SCCA/USAC Formula 5000 Championships in a Lola T330/332C prepared and entered by the Carl Haas and Jim Hall partnership. His rivals over this period included Mario Andretti, Al Unser, Jody Scheckter, Jackie Oliver, and Alan Jones, among others.
At the start of the 1977 season, following the conversion of Formula 5000 into the new Can-Am series with revised bodywork regulations, Redman suffered a catastrophic accident at Circuit Mont-Tremblant during the first day of practice. The car became airborne at approximately 160 mph, rose to a height of around forty feet, and landed inverted. Redman sustained broken bones and brain bruising and was declared dead at the scene; the ambulance transporting him suffered a tyre blowout en route to hospital. He recovered over nine months.
Redman returned to racing spectacularly, winning the 12 Hours of Sebring in 1978 in a Porsche 935. He continued with Dick Barbour Racing in 1979 and 1980. In 1981 he won the inaugural IMSA race at Laguna Seca in a new Lola T600 and went on to take the IMSA Camel GTP Championship that season. His final season of professional racing came at the age of 52 in 1989, when he drove for the Aston Martin works team in the World Sports Prototype Championship.
Road America hosts an annual vintage and historic racing event, The WeatherTech International Challenge with Brian Redman, which has grown into one of the largest and most prestigious meetings of its kind in the United States. Redman has been inducted into the Daytona International Hall of Fame, the Sebring Hall of Fame, the Talladega Hall of Fame, the Motor Sport Hall of Fame in the United Kingdom, and the Long Beach Pavement of Fame. He later co-managed the Redman Bright racing team and remains active in the motorsport community as a regular attendee at historic events.