After obtaining his Master's Degree in Musicology at the University of Oslo in 1971, Bjørklund studied composition with Finn Mortensen at the Norwegian Academy of Music (1971–1973).
Bjørklund wrote a number of commissioned works for choirs, orchestras and chamber music as well as solo settings.
The latter was recorded by the Trondheim Soloists and featured on the 2008 release Divertimenti, an album that received three 2009 Grammy nominations.
He also wrote a series of works on commission for chorus, orchestra and various solo and chamber music groups.
Among these are: Ole Edvard Antonsen, Christian Lindberg, Oslo Philharmonic Orchestra, The Chilingerian String Quartet, Trondheim Soloists, Marianne Thorsen, Nidaros Cathedral Boys' Choir, Aage Kvalbein, Stig Nilsson, Trondheim Symphony Orchestra and Bjarne Fiskum.