[1] Gudmundsson was born in Reykjavik, Iceland, the son of a frame-maker and art dealer Gudmundur Árnason and his wife Áslaug Sigurdardóttir.
He studied at the Icelandic College of Arts and Crafts, Reykjavik and at the Academie '63 (later De Ateliers '63) in Haarlem.
After returning to Iceland in 1966, with his wife and son, he became part of the Sύm group of artists, who had no single philosophy but shared characteristics with the international Fluxus movement and recognised the importance of a playful, innovative environment.
In the 1980s and 1990s Gudmundsson's practice focussed on making sculptures starting with works such as Het Grote Gedicht (The Great Poem) (1980–81) and Stella Maris, Kantadorum (1981).
Gudmundsson has exhibited widely internationally and had his first solo show in the UK at the Baltic Centre for Contemporary Art in Gateshead in 2003.