[1] Birgir was born in Akureyri, Iceland, before moving with his family to the capital city of Reykjavík at a young age.
[3] Birgir debuted with KR in February 1981 at the age of 15, becoming one of the youngest players to play in the Úrvalsdeild karla.
[2] After two years in the States, Birgir moved back to Iceland an initially planned to play for his hometown team Þór Akureyri in the second-tier 1. deild karla.
[8] During the 1989, Birgir announced that he would sign with Þór Akureyri but later renegaded on his decision and continued to play for KR.
[11][12] After retiring following the 1999–2000 season, where he led the league in free throw percentage, he returned to Skallagrímur in March 2001.
He served as an assistant to Yngvi Gunnlaugsson with Valur for the 2010–2011 season in the 1. deild and helped the team to promotion to the Úrvalsdeild.