Born 1663 at Kvennabrekka in Dalasýsla, western Iceland, Árni went to Denmark to study at the University of Copenhagen where he became an assistant of Royal Antiquarian Thomas Bartolin for six years. He travelled in Germany for two years and, upon his return to Denmark in 1697, was made the secretary of the Royal Danish Archives. At age 48, he became professor of Danish Antiquities at the university.
In 170, returned to Iceland, remaining there for ten years before returning to Copenhagen where he spent the remaining years of his life as a professor and librarian.
He devoted most of his life to collecting manuscripts, principally those of his native Iceland, but also those of other Nordic countries. His collection, the largest single collection of its kind, is known as the Arnamagnæan Manuscript Collection.
He was depicted on the now obsolete 100 Icelandic króna banknote.
Educational institutions in both Copenhagen and Reykjavik are named after him, the Árni Magnússon Institute in Reykjavík and The Arnamagnæan Institute in Copenhagen, which preserve and conduct studies on the manuscripts in the collection.