Christensen built an exceptional karting record during his junior years. He won the Nordic ICA Junior Championship in 2004, then gathered both the Nordic and European ICA Junior titles in 2005. Moving to Formula A class in 2006, he achieved second place in the Formula A World Championship and won the German Kart Championship twice, adding the Macau International Kart Grand Prix Formula A. He repeated as German Kart Champion in 2007 and won the KF1 South Garda Winter Cup.
Christensen made his open-wheel debut at the 2008 Formula BMW Europe season, with a race at Barcelona in support of the Spanish Grand Prix. He was involved in a serious-looking incident early in the season when he flipped his car, but recovered to finish sixth overall and take the top rookie award. Moving to Mucke Motorsport for 2009, he started the year strongly with a win in the opening race and appeared the front-runner for the title, but ultimately lost results from five races — including three victories — after his team lost an FIA technical regulations appeal. He finished fourth in the final standings.
In 2010, Christensen became the first driver to join MW Arden for the inaugural GP3 Series season, representing his final step in open-wheel single-seater racing before turning his focus toward sportscars.
Christensen joined the Porsche young driver program in 2012. He finished seventh in the 2012 Porsche Carrera Cup Germany and sixth in the 2013 Porsche Supercup before earning a promotion to full factory driver status in 2014.
In his debut factory season, Christensen raced in the WeatherTech SportsCar Championship alongside Patrick Long in the GTLM class, winning the 12 Hours of Sebring and the North American Endurance Cup. In 2015, he moved to the FIA World Endurance Championship with Manthey Racing alongside Richard Lietz in the GTE-Pro class, contributing to Porsche's manufacturers' championship win and finishing fourth in the drivers' standings.
His greatest achievement came in the 2018-19 FIA World Endurance Championship season, when he co-drove a Porsche 911 RSR to overall GTE-Pro victory at the 24 Hours of Le Mans.
For the 2023 WEC season, Christensen moved to Porsche Penske Motorsport's new Hypercar programme, partnering Dane Cameron and Frederic Makowiecki in the Porsche 963. He continued in the same role for the 2024 season alongside Makowiecki and Matt Campbell, competing at the top level of endurance racing.
Christensen's path from dominant karter to Le Mans winner is one of the more consistent developmental arcs in modern sportscar racing. After a near-miss championship in Formula BMW curtailed by a regulations dispute, he re-focused on endurance racing and found sustained success through the Porsche factory structure, earning both Le Mans victory and multiple championship wins across IMSA and WEC competition.