Kjellson and guitarist Ivar Bjørnson are the founding and only constant members of the band, as well as the main songwriters.

He has released sixteen studio albums with Enslaved and won five Norwegian Spellemann Awards with the band.

In 1996, Kjellson and Bjørnson together with Infernus and Tormentor of Gorgoroth created the short-lived thrash metal band Desekrator, which disbanded in 1999.

In 2009, Kjellson contributed along with Enslaved colleagues Isdal and Herbrand Larsen, and American actress Laraine Newman, in the animated television series Metalocalypse as one of "The Klokateers".

[9][10] Kjellson has stated in multiple interviews his opinion on the 1990s church burnings in Norway, mentioning in the documentary film Metal: A Headbanger's Journey that: