Born and raised in Arendal, Olsen received his degrees in philology at Royal Frederick University in Kristiania, where he became a protége of Sophus Bugge.

During the German occupation of Norway in World War II, Olsen served as dean at his university and was involved with the Norwegian resistance movement.

Olsen subsequently studied philology at Royal Frederick University in Kristiania, where he took courses in Latin, Greek, German and Norwegian.

[1][2] Bugge was widely considered Norway's greatest philologist at the time, but was in the process of losing his eyesight, and Olsen served as his assistant since 1902.

[2] After Bugge's death, Olsen succeeded him in 1908 as Professor of Old Norwegian and Icelandic Literature at Royal Frederick University.

He supervised the education of generations of Norwegian academics and teachers,[3] and together with scholars such as Carl Marstrander, Olsen developed Royal Frederick University into one of the world's leading institutions on Germanic philology.

The first issue included his inaugural lecture on the Skírnismál, in which he presented parallels between Njörðr of Norse mythology and Nerthus mentioned by Tacitus.

[6] Two of his best known publications are Hedenske kultminder i norske stedsnavne (1915) and Ættegård og helligdom (1926), which used toponymic evidence to examine Old Norse religion; these pioneering works made significant contributions to its scholarship.

[1] Notably, the evidence presented by Olsen showed that the Norse gods were venerated not only as creatures from another world, but as powers intertwined with the environment of the people.

His Ættegård og helligdom was eventually translated into English and published under the title Farms and Fanes of Ancient Norway (1928).

[2] Gabriel Turville-Petre mentions Olsen along with Georges Dumézil and Jan de Vries as one of the most influential scholars on Old Norse religion.

Olsen's research on Scandinavian place names were instrumental in restoring confidence in Icelandic literature as a useful source of information on Old Norse religion.

Between 1941 and 1960, he published his subsequent Norges innskrifter med de yngre runer (Norwegian Inscriptions in the younger Runes) in five volumes.

[1] During the German occupation of Norway in World War II, Olsen distinguished himself as a fierce opponent of Nazism, and was close to the resistance movement at the University.