After having completed high school, Kverndokk enrolled at the Norwegian Academy of Music from which he graduated with diploma in 1994, having studied under the tutorship of Olav Anton Thommessen, Lasse Thoresen and Alfred Janson.
2002 saw the premiere of musical Dangerous Liaisons, a work based on Pierre Choderlos de Laclos's novel of the same name, at the Theater Pforzheim, Germany.
In autumn 2003, Kverndokk and Wiik’s musical Homeless, based on Hector Malot’s novel, premiered at Oslo’s Det Norske Teatret.
Autumn 2015 saw the release of the album Fuge der Zeit, which featured a mass penned by Kverndokk for Nordic Voices based on the work Missa Brevis, originally commissioned by the 2002 Fartein Valen Dagene.
[6] Kverndokk's most recently composed orchestral work is Symphonic Dances written for the Stavanger Symphony Orchestra in commemoration of Norway's Centenary Celebration of its Constitution in 2014.
Kverndokk's latest chamber work, Offertorium for clarinet, cello and piano, was premiered at the Ultima Oslo Contemporary Music Festival in September 2015.