Stewart Grand Prix had competed since 1997, the team founded by former World Champion Jackie Stewart and his son Paul Stewart in partnership with Ford. By 1999, Barrichello was beginning his third season with the team while Herbert arrived from Sauber as a new signing. The SF3 was powered by the new Cosworth CR1 V10 engine, described as notably compact and technically advanced, and was launched on January 7 at the Autosport International show at Birmingham's NEC.
Development work began during 1998, with test sessions at Silverstone involving several drivers including Luciano Burti, Mario Haberfeld, and Jos Verstappen. Gary Anderson joined as Technical Director during an internal reshuffle that also saw Paul Stewart become deputy chairman. The car's livery continued the team's established white scheme with a Tartan stripe running down each side of the cockpit, and HSBC served as primary sponsor alongside heavy Ford branding on the engine cover.
A significant development package was released ahead of the British Grand Prix, incorporating undertray modifications, revised sidepods, raised exhausts, and further engine refinements.
The 1999 season opened poorly in Australia when both cars suffered oil leaks causing fires before the formation lap, forcing the start to be aborted. Herbert did not start at all, while Barrichello drove the team's spare car and eventually recovered to fifth place despite a stop-go penalty for speeding in the pit lane.
Barrichello provided the season's early highlight in Brazil, qualifying third and briefly leading his home Grand Prix before retiring with engine failure. The SF3 scored its first podium at San Marino, where Barrichello finished third behind Michael Schumacher and Mika Hakkinen. Herbert was running fifth when his engine failed with three laps remaining.
Further mechanical misfortune dogged both drivers through Monaco and Spain. Barrichello was disqualified in Spain for a technical infringement involving the undertray and skid tray, while Herbert had yet to be classified as a finisher through the first five races of the year. Herbert's luck changed in Canada, where he scored two points with fifth place.
A high point came at the French Grand Prix, where Barrichello qualified on pole — only the second pole of his career — and finished third while also setting the race's fastest lap.
The season's defining moment came at the European Grand Prix at the Nurburgring. Herbert, starting fourteenth, won the race in circumstances that involved a changeable track and numerous retirements ahead of him. Barrichello finished third, giving Stewart a one-two podium. It was the team's only Formula One victory, achieved in their penultimate season.
In Malaysia, Barrichello and Herbert finished fourth and fifth. Ferrari's cars were subsequently disqualified from the results on technical grounds, temporarily promoting the Stewart pair to second and third, though the FIA ultimately reinstated the original placings on appeal.
The team's final Grand Prix came in Japan, where both cars finished, with Barrichello completing his last race for the outfit before signing with Ferrari. The team secured fourth place in the Constructors' Championship with 36 points.
Barrichello was the team's primary points scorer throughout 1999, his pace and racecraft consistently extracting the best from the SF3. His French Grand Prix pole position was a measure of how far the team had come. Herbert's European Grand Prix victory, meanwhile, stood as one of the more unexpected results of the season given his grid position.
Ford's acquisition of the team was announced during the season. The SF3 continued in use after the championship ended: Eddie Irvine, who would join the rebranded Jaguar team for 2000, tested it at Jerez in December 1999. In 2000, the car was fitted with Michelin tyres as part of development preparation, and was driven by Le Mans winner Tom Kristensen.
The SF3 remains the only car to have won a Formula One race under the Stewart Grand Prix name, and it closed out a short but significant chapter in British motorsport history.