Early musical studies with Gunnar Sigurgeirsson and then enrollment at theReykjavík College of Music where his teachers were Hermina Kristjansson, Jon Nordal, Arni Kristjansson (piano), and Thorkell Sigurbjornsson (composition). Piano studies with Barry Snyder at the Eastman School of Music (1974-1975).
Studies in composition with Finn Mortensen, electronic music and sonology with Lasse Thoresen and sonology with Olav Anton Thommessen in Norway in the following year.
Studied composition with Ton de Leeuw in Amsterdam from 1976-1978. Since 1980 Birgisson has been living in Reykjavík, where he is an active composer, performer and music teacher. He has composed solo works, chamber works, symphonic pieces and choir music.
He has written a series of three concertos especially for CAPUT: CAPUT Concerto No. 1 for chamber orchestra (commissioned by the Reykjavík European City of Culture in the Year 2000, CAPUT Concerto No. 2 (2002) for ensemble and three percussion soloists (Eggert Pálsson, Pétur Grétarsson and Steef van Oosterhout) and Piano Concerto No. 2 for piano and ensemble which was also written especially for pianist Vikingur Olafsson who premiered the work in 2006 at the Nordic Music Days in Reykjavík.
In 1996 he was commissioned by NOMUS to compose In a Magnetic Field jointly for CAPUT, Avanti!, BIT 20, Composers Ensemble, Sonanza and Storströms Kammerensemble.