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Varhaug began his motorsport career in karting in 2005, where he finished fifth in the Norwegian Championship ICA Junior. He also finished fourth in the Viking Trophy ICA Junior class. The following year he again won the Norwegian Championship ICA Junior.
Varhaug switched to single-seaters in 2007, where he participated in the Swiss formula Renault 2.0 for the team Jenzer Motorsport. In the entire season he achieved seven podium places, including four race wins, to finish as runner-up in the Championship behind the Czech driver Adam Kout. He also competed in some races in the Italian Formula Renault 2.0 and Formula Renault Northern European Cup.
Varhaug continued with Jenzer Motorsport driving in 2008 in both the Eurocup Formula Renault 2.0 and Italian Formula Renault 2.0. He finished fifteenth in the Eurocup, with a best result of fifth place in the second race at Estoril.  In Italy he finished all 14 races in the points and with three wins, he is safe for the title. 
In Varhaug stepped over to the 2009 International Formula Master, still for Jenzer Motorsport.  he finished fifth in the total rookiekampioenschap and second in the State behind Alexander Rossi. He earned five podium finishes and a pole position at the Automotodrom Brno.
Varhaug drives in 2010 in the new GP3 serieswith Jenzer Motorsport.  he drives it in addition to the Swiss Simon Trummer and Nico Müller. After he qualified in second place, won the very first GP3 Varhaug inBarcelona was allowed to race and with Robert Wickens and Esteban Gutiérrez to the stage.  it turned out that this would be his only points of the season and ended up as a result, the thirteenth in the Championship with 10 points. He was originally third in the second race at Spa-Francorchamps, but later he was restored to the fifteenth place because he had the safetycar in. Also he put down the fastest lap on theAutodromo Nazionale Monza, but got no championship point here for because he is not in the top 10 ended.
Varhaug reed in 2011 in the GP2 Asia Series for the DAMS team alongside Romain Grosjean. With the sixth place in the last race at the Autodromo Enzo e Dino Ferrari he finished thirteenth in the Championship with one point, while the title of Grosjean caused DAMS also won the team championship.
Varhaug reed in 2011 also in the main GP2 Series Championship for DAMS in addition to Grosjean. While Grosjean also won the title here, scored Varhaug no point leaving him 23rd in the Championship ended.
Because he lost his seat at DAMS, stepped over to the 2012 Varhaug in Auto GP for the team Virtuosi UK. With victories at Monza, the Sonoma Raceway Hungaroring and he finished second in the Championship with 183 points, 38 points behind champion Adrian Quaife-Hobbs.