Ólafur was born in Birtingaholt in Hrunamannahreppur, Iceland, the son of Skúli Oddleifsson and Sigríður Ágústsdóttir.

In 1960, he was appointed as the first youth representative of the National Church and in 1964 became pastor of Bústaðarkirkja in Reykjavík.

His time as bishop saw a great transformation towards more independence for the National Church.

At the time, he was also a board member of the Lutheran World Federation and chaired the administration of the Ecumenical Organisation in Strasbourg.

[1] However, after his death, in 2010 his daughter Guðrún Ebba Ólafsdóttir attended the Church Council and disclosed that Ólafur had sexually abused her for many years.