Salo competed in the British Formula 3 Championship in 1989 with Alan Docking Racing, using a Reynard Alfa Romeo package that was not the field's most competitive. He returned with the same team in 1990, switching to a Ralt chassis and finishing second in the championship behind his compatriot and fierce rival Mika Häkkinen. He then raced in Japan across several seasons before returning to Europe for his Formula One opportunity.
Salo made his Formula One debut at the 1994 Japanese Grand Prix for Lotus and contested the season finale in Australia. Following Lotus's collapse, he joined Tyrrell for 1995 and remained with the team for three seasons. He scored points on several occasions, with a notable result coming at the rain-shortened 1997 Monaco Grand Prix, where he completed the entire race without refuelling to finish fifth ahead of the faster Giancarlo Fisichella. He moved to Arrows for a promising 1998 campaign but had no full-time drive heading into 1999.
Salo's 1999 season began at British American Racing as a stand-in for the injured Ricardo Zonta across three races, achieving a seventh-place finish at San Marino — BAR's best result of the year. A more significant opportunity arose when Michael Schumacher broke his leg at the British Grand Prix, and Salo was selected to partner Eddie Irvine at Ferrari for the remainder of the season.
At the German Grand Prix, his second race in the Ferrari, Salo led the race and appeared set to score his only Formula One victory. However, team orders directed him to give the lead to Irvine, who was engaged in a championship battle with Häkkinen. Salo duly moved aside. Irvine, in a gesture of gratitude, handed his victory trophy to Salo after the race. Salo also finished third at the Italian Grand Prix at Monza, ahead of Irvine. The two podiums and ten points Salo scored in six races contributed directly to Ferrari's Constructors' title by a four-point margin.
Salo raced full-time with Sauber in 2000 and finished 11th in the Drivers' Championship before joining the Toyota team in preparation for their 2002 Formula One entry. He scored two points for Toyota in their debut season, finishing sixth at the Australian Grand Prix — the first driver since JJ Lehto at the 1993 South African Grand Prix to score points on a team's Formula One debut. He was released by Toyota at the end of 2002, the team having been dissatisfied with his performance. Salo scored 33 championship points in total across his Formula One career.
Salo's post-Formula One career produced sustained success in long-distance racing. He drove the Audi R8 at the 2003 12 Hours of Sebring and later became aligned with Ferrari's sportscar programme. After winning the 24 Hours of Spa in the GT2 class in 2006, he joined Risi Competizione and won the GT2 class championship in the American Le Mans Series in 2007 alongside Jaime Melo, the pair taking eight class wins from twelve races. Salo and Melo won the GT2 class at the 24 Hours of Le Mans in 2008, and Salo returned to win Le Mans again in 2009, also winning the 12 Hours of Sebring and the Petit Le Mans in the same year with Risi Ferrari. In 2014, partnering Craig Lowndes, John Bowe, and Peter Edwards in a Ferrari 458 Italia GT3 for Maranello Motorsport, he won the Bathurst 12 Hour.
Salo has commentated on Formula One races for MTV Oy in Finland since 2005, following a pattern established by fellow Finns Keke Rosberg and JJ Lehto. Since 2011 he has hosted the Finnish television programme Virittäjät. He lives in Tallinn, Estonia, and his godson Jesse Krohn competes in the IMSA SportsCar Championship.