Kjelbotn made his international debut at FIS junior competitions in 2003. Shortly afterwards, he started in the B World Cup of Nordic Combined . At the Junior World Championship 2005 in Finland Rovaniemi Kjelbotn reached with the team in the team event in fifth place. In the sprint he came in 32nd place. A year later at the Junior World Championships in Kranj in 2006 he won the bronze medal with the team. In the sprint he achieved a 13th place, in the Gundersen a 16th place. After he achieved consistently good performances in the B World Cup, Kjelbotn made his debut in the Nordic Combined World Cup on December 6, 2008 in Trondheim . Already in the second World Cup he managed to win World Cup points by finishing 26th. With the points gained, he finished 72nd in the overall World Cup standings with the Italian Armin Bauer at the end of the 2008/09 season . Despite this point gain, he has since continued to compete mainly in the Continental Cup and is rarely invited to World Cup competitions, in which he then remained unsuccessful. In the 2012/13 season, Kjelbotn, whose strengths can be found in the special jumping, improved form before a cruciate ligament rupture forced him to end the season prematurely. He had his best World Cup season in the winter of 2013/14 when he reached thirtieth place in the overall standings.
In April 2017, Kjelbotn announced the end of his career.
Coaching career
Kjelbotn has been working part-time for the Norwegian Ski Association since the 2019/20 season as the head coach of the newly founded female national team in Nordic combined. He is also a trainer for the Granåsen Ski Team in Trondheim .