Björn was born in Ferjubakka í Borgarhreppi in 1911, son of Guðmundur Andrésson (31 October 1870 – 3 January 1969) and Ragnhildur Jónsdóttir (2 September 1877 – 2 July 1943).
Borgarhreppur was formerly a rural parish (hreppur) in Mýrasýsla county, west Iceland, named after the ancient farm and church estate Borg á Mýrum which was occupied by Skallagrímur Kveldúlfsson, one of Iceland's original settlers.