He was a teacher at the Akureyri Grammar School and the College of Navigation in Reykjavík, becoming a curator at the National Museum of Iceland in 1945 and its Director in 1947, a position he held until the 1968 presidential election.

This no doubt gave him the incentive needed to run in the 1968 presidential election as a politically non-affiliated candidate.

Starting as the underdog in the 1968 presidential election, running against Ambassador Gunnar Thoroddsen who initially had a 70% lead in the opinion polls, Kristján won 65.6% of the vote on a 92.2% voter turnout.

In 1980 he decided not to run for another term, wanting to devote his remaining years entirely to continuing his lifelong academic work.

[2] His son Þórarinn Eldjárn is one of Iceland's most popular authors, specializing in short stories, but also writing poetry and an occasional novel.