The team's roots trace to 1988, when Paul Stewart bought the Gary Evans Motorsport team and established Paul Stewart Racing. That outfit entered British Formula 3 in 1989 with ten employees and Camel sponsorship, winning at Snetterton. Through the early 1990s, Paul Stewart Racing expanded into Formula Vauxhall Lotus, Formula 3, and Formula 3000, accumulating twelve titles and 119 race wins across categories.
Jackie Stewart declined to enter Formula 1 until January 1996, when he secured a five-year development deal with Ford to run as a factory team. Ford had previously supplied engines to Sauber; the arrangement with Stewart would be a full works partnership. Malaysia's government also became a backer, using the team to promote the country. The new team was headquartered in Milton Keynes and consulted with designer John Barnard on a budget reportedly around £24 million.
The team's first car, the Stewart SF01, was launched in December 1996. Rubens Barrichello and Jan Magnussen drove at the season opener in Australia. The season's standout result came at the Monaco Grand Prix, where Barrichello finished second in wet conditions. Otherwise the SF01 was a midfield runner plagued by the Ford Zetec-R V10's fragility; the team managed only eight classified finishes from a possible 34. Stewart ended the year ninth in the constructors' championship with six points.
The updated Stewart SF02 failed to deliver the hoped-for progress. Points were scarce, with neither Barrichello nor the mid-season replacement Jos Verstappen — who arrived after Magnussen's removal — able to reach the podium. Barrichello's fifth in Spain was the first points finish, and a Canadian double-points result for Barrichello and Magnussen in fifth and sixth was the season highlight. The team finished eighth in the championship. Technical director Alan Jenkins departed and was replaced by Gary Anderson from Jordan.
After Ford acquired Cosworth in 1998, the team received a brand-new engine for the Stewart SF3. The car was immediately competitive, though overheating problems eliminated both cars on the Australian grid. Barrichello qualified on pole in France — the team's only pole position — while Johnny Herbert gave the team its sole race victory at the European Grand Prix at the Nürburgring, held in wet conditions after rivals crashed or pitted for tyres. Barrichello finished third in the same race. Stewart finished fourth in the constructors' championship with 36 points, ahead of former world champions Williams and Benetton.
Herbert also played an unwitting role in the drivers' championship at the Malaysian Grand Prix. Running third behind the Ferraris of Michael Schumacher and Eddie Irvine, a late mistake allowed Mika Häkkinen past. The Ferraris were initially disqualified for car irregularities, a result that briefly awarded Häkkinen extra points — though Ferrari won on appeal and the original result was reinstated. Häkkinen ultimately took the title in Japan regardless.
Ford purchased the team outright at the end of 1999, renaming it Jaguar Racing for 2000. The Jaguar years proved difficult commercially, and in 2004 Ford sold the operation to energy drink company Red Bull GmbH. Rebranded as Red Bull Racing from the 2005 season, the same Milton Keynes facility went on to win multiple Formula One World Constructors' Championships through the 2010s and 2020s. Stewart Grand Prix's three-season run is therefore directly ancestral to one of the sport's most successful modern operations.