Norum made his debut in the World Cup in November 2008 in Gällivare , where he finished 86th over 15 km freestyle and finished 22nd and last with the fourth Swedish relay. He achieved his first World Cup points in March 2012 with 18th place in the sprint in Lahti .
In the Scandinavian Cup 2011/12 he achieved two top ten placings with fifth place in the sprint in Nes and ninth place in the 30 km freestyle mass start race in Madona and finished eighth in the overall standings.
At Rollerski World Championships , Norum won bronze in the relay in 2009, in 2013 silver in the 20 km freestyle and bronze in the team sprint, and in 2015 silver in the 25 km freestyle mass start race and again bronze in the team sprint. In 2015, Norum also won the Rollerski World Cup . In the summer of 2016, he won the Rollerski World Cup 2016 six times and again won the overall ranking. Also in summer 2017 he won the Rollerski World Cup with three thirds, one second and three first places . At the 2017 Rollerski World Championships in Sollefteå , he won the bronze medal in the 20 km mass start race. In 2018 he won the Rollerski World Cup for the fourth time in a row with three second and three first places. At the Rollerski World Championships in Madona in 2019 , he and Victor Gustafsson won the bronze medal in the team sprint.