[1] He played twenty seasons in the Icelandic top-tier league with Ármann and helped the club to its first and only men's national championship in 1976.
[5][6] Birgir played his first senior team game for Ármann in 1958, at the age of 16,[5] and spent twenty seasons with the club, winning the Icelandic Basketball Cup two times, in 1975 and 1976.
[11][12] In June 1977 Birgir left Ármann and took over as head coach of ÍS.
[21] On 8 November 2000 Birgir's 27-year-old son Einar Örn Birgisson, a former football player, went missing.
[22] A week later, Atli Helgason, Einar's business partner and former teammate, confessed to his murder and hiding his body near Grindavík.