Solberg grew up in Spydeberg and, like his younger brother Petter, began in bilcross — the Norwegian low-budget rallycross discipline similar to Swedish folkrace — before transitioning fully to rallying in the mid-1990s. Between 1999 and 2003 he won the Norwegian Rally Championship five consecutive times, establishing himself as the dominant force in domestic competition and catching the attention of WRC teams.
Solberg made his WRC debut as a privateer before earning a contract with Bozian Racing for the 2004 season, competing in the Peugeot 206 WRC. At the 2004 Swedish Rally he scored his first WRC points, finishing sixth — his best result and only points finish that year.
For 2005 he was signed by the BP Ford World Rally Team to compete at seven rounds alongside Toni Gardemeister and Roman Kresta. His best result of the season came at the Cyprus Rally, where he beat both team-mates to finish fourth. He ended the year fourteenth in the drivers' championship with nine points.
In 2006, partnered with Manfred Stohl at OMV Peugeot Norway WRT in the Peugeot 307 WRC, Solberg competed in twelve of the sixteen WRC rounds. He achieved his first career podium at the Rally of Turkey, finishing third, and scored six further points-paying results to end eighth in the drivers' standings.
Solberg moved to the Stobart VK M-Sport Ford Rally Team for 2007 with a full-time drive. He secured his second career podium at the Rally Norway — the event's first appearance on the WRC calendar — finishing third in his Ford Focus RS WRC 06. Later that season he took a third podium at the Rally Japan, ending the year sixth in the championship ahead of Chris Atkinson and Jari-Matti Latvala.
He remained at Stobart for the 2008 and 2009 seasons. In 2009 he delivered his career-best sustained run, finishing fourth in both the season-opening Rally Ireland and the following Rally Norway, then adding a podium in Argentina — his fourth career top-three finish — behind Sébastien Loeb and Dani Sordo, plus a further podium in Poland.
In 2010 and 2011 Solberg continued with the Stobart team on a reduced schedule, alternating between the Ford Focus RS WRC and the Ford Fiesta S2000. His co-driver throughout most of his WRC career was Ilka Minor; Stéphane Prévot deputised during Minor's injury.
Solberg competed for the privateer Go Fast Energy World Rally Team in the first half of 2012 alongside Matthew Wilson, but the team folded after the Swedish Rally left the series. He made a return to the WRC at the 2013 Rally Sweden — his first competitive start in over a year — co-driven by Emil Axelsson in an M-Sport Fiesta RS WRC. The entry finished eighth, and it was among his last appearances at WRC level.
Beyond the stages, Solberg appeared on the BBC television programme Top Gear, where he rallied a Mitsubishi Lancer Evolution against the Norwegian bobsleigh team at the Lillehammer Olympic Bobsleigh and Luge Track — a 1,365-metre course with sixteen turns and an 8.5 per cent average gradient. With presenter James May as co-driver, Solberg posted a time of 1:02:24 in the Evo, narrowly losing to the bobsled (with Richard Hammond aboard) which clocked 59.68 seconds.
Solberg's WRC career produced four podium finishes and consistent points-scoring runs across nearly a decade of front-line competition, and he was a reliable midfield presence during the competitive mid-2000s era of the championship. As a member of the Solberg family — the most decorated Norwegian rally dynasty — he played a significant part in normalising Norwegian dominance at the top of world rally sport.