After passing his examen artium in 1899 at the Kongsbakken Upper Secondary School, he moved to Oslo, where he worked as a teacher (among other places, at Brandbu Middle School from 1907 to 1909) while studying. He received his university degree in 1910 with a thesis titled Senjen-maalet. Lydverket i hoveddrag (The Senja Dialect: Phonology and Main Features, published 1913), after which he taught in Arendal from 1910 to 1913.
In 1918 he went on partial leave to pursue a university scholarship that enabled him received his Doctor of Philosophy in 1921 with the dissertation Bokmål og talemål i Norge 1560–1630 (Standard Language and Dialects in Norway from 1560 to 1630).
In 1922 he became a professor at the newly established Norwegian College of Teaching in Trondheim (where he was appointed chancellor in 1936), and the same year he was elected to the Norwegian Academy of Science and Letters. He became president of Royal Norwegian Society of Sciences and Letters in 1932.
Together with Halvdan Koht (also from Tromsø), Johan Bojer, Gustav Natvig-Pedersen, Arne Bergsgård, and Martin Birkeland, in 1934 Iversen was appointed to a committee whose recommendations led to the 1938 orthographic reform and the common language variety known as Samnorsk. He was also a recipient of the Swedish Order of the Polar Star.
Iversen died in Trondheim.
At Uppsala University, he became a member of the Royal Gustavus Adolphus Academy in 1933, a member of the Upsala Linguistics Society in 1952, and a member of the Royal Society of Humanities at Uppsala in 1959, and he received an honorary doctorate from the university in 1954.