Bragi studied Spanish at the University of Iceland and the University of Granada. He has had a number of different jobs in Reykjavík, at the post office, in a bank and in a record store. He was also a member of the Sugarcubes, and toured with them in Europe and America.
Bragi's first published work, the poetry collection Dragsúgur (Draught), appeared in 1986. Since then, he has published other books of poetry, short story collections, plays and novels. His first novel, Hvíldardagar (Days of Repose) was nominated for the Icelandic Literary Prize in 1999 and the next one, Gæludýrin (The Pets) also in 2001. He received the DV Cultural Prize for the novel Samkvæmisleikir (Party Games) in 2004 and his novel Sendiherrann (The Ambassador) was nominated for the Nordic Council's Literature Prize in 2008.
Bragi is one of the founders of the publishing company Smekkleysa (Bad Taste) which has mostly put out music and organised various kinds of events.