Tauranac based the BT24 on the BT23 Formula Two car, making it notably light and compact relative to the opposition. He continued to use a spaceframe chassis — by 1967 unique among Formula One designers, virtually all of whom had moved to monocoques — maintaining his established belief that a well-built spaceframe was no less stiff than contemporary monocoques and significantly easier to repair.
The BT24 was designed around Repco's new RB740 V8 engine, an entirely new design built entirely by Repco rather than adapted from the Oldsmobile block of the 620 series. Tauranac had specifically requested that Repco design the engine with in-vee exhausts, which reduced frontal area and solved the packaging problem that had plagued the 620 — its exhausts had been routed outward and through the spaceframe, complicating design work considerably. The 740's central exhaust layout was a meaningful engineering step forward.
The BT24 made its first appearance during practice for the 1967 Dutch Grand Prix, the same event at which Lotus debuted the technically advanced Lotus 49. The comparison appeared to flatter Lotus — the BT24 seemed almost conservative in contrast — but as the season progressed, Brabham's superior reliability proved decisive.
Jack Brabham elected to race his proven BT19 at the Dutch round rather than introduce the untried new car, and the BT24 made its race debut at the Belgian Grand Prix. From that point, with reigning champion Brabham and Denny Hulme sharing driving duties, the BT24 took three race victories to Jim Clark's four in the Lotus 49. However, six second places, two thirds, a fourth, and a fifth gave the Brabham team the Constructors' Championship comfortably, while Hulme edged team owner Brabham to the Drivers' title by five points.
The BT24 also won the prestigious 1967 International Gold Cup at Oulton Park in Jack Brabham's hands.
Two of the three BT24 chassis were raced by Brabham and Jochen Rindt at the 1968 South African Grand Prix, the opening race of the new season, before the BT26 arrived to replace them. Both cars were then sold to local South African teams rather than being repatriated. Sam Tingle and Basil van Rooyen finished third and fourth in that year's South African Formula One Championship with these chassis. Tingle continued racing his BT24 in local events as late as January 1970, and entered the 1969 South African Grand Prix — the last World Championship appearance of a standard BT24.
The third chassis had a more varied career. After two outings for Rindt and a one-off appearance by Dan Gurney in 1967, Kurt Ahrens Jr. hired it for the 1968 German Grand Prix. Frank Williams then acquired and modified it with BT26-style wings and a 2.5-litre Cosworth DVW V8 for the 1969 Tasman Series, where Piers Courage drove it to a win at Teretonga Park in New Zealand and several other strong results. Silvio Moser subsequently took over the car, fitting a 3.0-litre DFV and raced it in seven rounds of the 1969 Formula One World Championship, his best result a sixth at Watkins Glen.
The BT24 gave Brabham and Repco their second consecutive Constructors' Championship and Denny Hulme his only World Drivers' title. As the tortoise to Lotus's hare in 1967, it embodied the Brabham philosophy: a light, simple, reliable package that accumulated points throughout the season when more spectacular machinery failed. Its long life in private hands — across South Africa, the Tasman Series, and Moser's 1969 Formula One campaign — speaks to the durability of Tauranac's spaceframe engineering approach.