Jón was born on a farm in Þingeyrar in Iceland's Northwestern Region and graduated from the Menntaskólinn í Reykjavík gymnasium in 1917.

He then studied natural sciences the University of Copenhagen in Denmark for two years, before moving to Norway, completing a cand.mag.

In November 1950, he founded the Iceland Glaciological Society [is], serving as its first chair and editor of its journal, Jökull.

[1] Through his observations and the annual lists of measurements published in Jökull, Jón helped standardize the names of Iceland's glaciers.

[3] In 1950, he published a brief description of glacial moss colonies, which he dubbed jökla-mýs (Icelandic for "glacier mice").