Davidson was born in Hemel Hempstead, Hertfordshire, and began kart racing at the age of eight. He won three British karting championships in 1993, 1994, and 1995, as well as an Italian championship, and finished runner-up in the Formula A European championship in 1996.
Moving to single-seater cars in 1999, Davidson won the 1600cc Kent class at the British Formula Ford Festival and the following year won the Formula Ford Festival outright at Brands Hatch. He also won the McLaren/Autosport Young Driver of the Year Award. In 2001, racing British Formula Three with Carlin, he finished second overall behind teammate Takuma Sato while winning the Formula Three Pau Grand Prix, the Spa Masters, and the FIA European Cup.
Davidson joined British American Racing (BAR) as a test driver in late 2000. When regular Minardi driver Alex Yoong was suspended in 2002, Davidson made his Formula One race debut, substituting for two Grands Prix — Hungary and Belgium — setting qualifying times within 0.6 seconds of teammate Mark Webber despite spinning out of both events.
He remained BAR's test driver through 2003 and into 2004, when the team could run a third car in Friday practice. Davidson frequently impressed paddock observers with his consistent times, and other teams regularly used his lap data for tyre degradation reference. He tested a Champ Car at Road America for Team KOOL Green in 2002 as part of a Honda tyre development programme.
In 2005, Davidson filled in for an unwell Sato at the Malaysian Grand Prix but retired two laps into the race with an engine failure. He continued as test driver in 2006 under Honda's ownership of the team, also making his debut as a television commentator at the 2006 Hungarian Grand Prix, standing in for Martin Brundle on ITV Sport.
On 15 November 2006, Super Aguri confirmed Davidson as a full-time race driver for 2007 alongside Takuma Sato, giving him a permanent Formula One seat for the first time. During the 2007 Canadian Grand Prix, Davidson was running third when his car struck a groundhog on the main straight, dropping him to eleventh and costing him what would have been his first points finish. At the Hungarian Grand Prix, a collision with Giancarlo Fisichella's rear suspension ended his race. He finished 2007 in 23rd position without scoring points. His career-best classified finish was eleventh, achieved at the Spanish, Canadian, and United States Grands Prix aboard the SA07.
Super Aguri retained Davidson alongside Sato for 2008, but the team withdrew from the championship on 6 May 2008 due to financial collapse, ending both drivers' Formula One careers mid-season. Davidson subsequently held test and simulator roles with Brawn GP and, when Mercedes-Benz bought the team in late 2009, continued in that capacity with Mercedes GP.
Davidson moved into sportscar racing from 2009, driving for Aston Martin Racing at Le Mans that year before joining Peugeot Sport for 2010. He co-led the 2010 12 Hours of Sebring to a Peugeot 1–2 finish alongside Alexander Wurz and Marc Gené, warming up for Le Mans, where their car suffered an engine failure while leading. Later in 2010 he won the 6 Hours of Silverstone for Peugeot.
In 2011, Davidson, Wurz, and Gené won the 6 Hours of Spa. He and Sébastien Bourdais then won the 6 Hours of Imola and the 6 Hours of Zhuhai, helping Peugeot clinch the Intercontinental Le Mans Cup championship for a second consecutive year.
When Peugeot withdrew from factory sportscar competition, Davidson signed with Toyota for the 2012 FIA World Endurance Championship. Five hours into the 2012 24 Hours of Le Mans, a collision between Davidson's Toyota TS030 Hybrid and a Ferrari GTE car at the end of the Mulsanne Straight sent his car airborne. The vehicle landed on three wheels before striking the barriers heavily. Davidson climbed out before being hospitalised with fractures to the eleventh and twelfth thoracic vertebrae.
He returned for a full 2013 season with Toyota, finishing third in the drivers' championship and second at Le Mans alongside Sébastien Buemi and Stéphane Sarrazin. In 2014, driving the new Toyota TS040 Hybrid, Davidson won four races alongside Buemi and claimed the 2014 FIA World Endurance Drivers' Championship. He also finished third at that year's Le Mans 24 Hours.
The 2017 season brought five victories with his Toyota co-drivers, but a sixth-place finish at Le Mans and absence from the Circuit of the Americas race contributed to a third-place championship finish. Davidson was subsequently moved aside within the No. 8 Toyota entry to accommodate Fernando Alonso's WEC campaign for 2018–19, and shifted into LMP2 competition with DragonSpeed and later Jota through the 2021 season, when he retired from professional racing.
Davidson joined the BBC as a co-commentator for Formula One on Radio 5 Live in 2009 alongside David Croft. When Sky Sports acquired British F1 broadcast rights in 2012, Davidson moved across as an analyst for race weekends. He has been a lead commentator on the FIA World Endurance Championship world feed since 2022. Davidson has also worked as an advisor and voice talent for Codemasters' official F1 video game series since 2009, appearing across eleven editions.