Hallgrímur was born on 5 April 1841 in Blöndudalshólar, Iceland, the son of Sveinn Níelsson, a member of parliament, and Guðrún Jónsdóttir.

In 1971 he joined and became a member of the Reykjavik Cathedral priests.

That same year he also married Elina Marie Bolette Fevejle.

They had four children, Friðrik, Guðrún, Sveinn and Ágústa.

[2] On 16 April 1889 he was appointed Bishop of Iceland and was consecrated on 25 May in Copenhagen.