[1][2] Karl was the son of Sigurbjörn Einarsson, Bishop of Iceland between 1959 and 1981 and his wife Magnea Thorkelsdóttir.

On 6 December 1974, he was appointed parish priest of Hallgrímskirkja in Reykjavík and was installed on 1 January 1975, a post he retained till 1997.

He served a pastoral ministry in Sweden from 1977 to 1978, and studied in the United States from 1988 to 1989.

On 6 September 1997 he was elected Bishop of Iceland and was consecrated on 23 November that year.

[3] Karl was the father of actor Guðjón Davíð Karlsson.