Sundby showed up on the international Cross-Country skiing scene in 2002 at FIS competitions in Gaalaa (NOR). A year later he took part in his first FIS Junior World Ski Championships in Solleftea (SWE). He cracked top 10 at his first competition finishing 8th in 30 km Mass Start Free. He scored his personal best at the Junior World Ski Championships one year later in Stryn (NOR) where he claimed 6th place in 10 km free.
World Cup debut came in 2005 in 50 km classic in Oslo but did not finish the competition. It took almost a year until he has shown up at another World Cup competitions in Oslo and Falun. In December 2006 Sundby earned his first World Cup points at the World Cup in La Clusaz, he finished 25th in 30 km Mass Start Free. In 2007 Sundby celebrated first World Cup podium being member of the victorious Norwegian relay team. In 2008 Sundby won first World Cup in Kuusamo, 15 km Classic.
In 2009 Sundby debuted at the World Ski Championships. In Liberec he claimed 24th place in 15 km classic. Two years later he was among the hot favorites for a medal in Oslo. He showed a very strong performance that was crowned with bronze medal in 15 km classic and gold medal in the relay.
Sundby has been classical technique specialist but has been working on the free technique as well and won the World Cup 2012/13 openener 15 km Free in Gällivare (SWE). At the FIS Nordic World Ski Championships in Val di Fiemme in 2013 he won silver medal in skiathlon and gold medal in the relay.
Additionally Sundby has won five Norwegian titles.
At the beginning of the 2011/12 season Sundby was struggling with health problems caused by irregular heartbeat.