Sigurbjörn was born in Meðalland [is] in Vestur-Skaftafellssýsla, where his father, Magnús Kristinn Einar Sigurfinnsson, was a farmer.

After graduating in 1931 from Menntaskólinn í Reykjavík, he studied in Sweden, qualifying in Greek, Classical studies, and history at Uppsala University in 1936 and earning his cand.

[1] On 22 June 1959 he was consecrated as Bishop of Iceland by his predecessor, Ásmundur Guðmundsson;[3] in September 1981 he was succeeded by Pétur Sigurgeirsson.

[4] He is credited with modernising the Church of Iceland, making it more ecumenical and international in outlook.

[1][6] Sigurbjörn published numerous books, including textbooks on the history of religion and the psychology of religious life, an analysis of the Revelation of St. John, Trúarbrögð mannkyns, a second edition of which was published in 1978,[7] a biography of Albert Schweitzer published in 1955, translations including hymns and the Confessions of St. Augustine, and a children's book titled Af hverju, afi.