Nordhagen was educated as an engineer in Oslo and worked as an apprentice to architect Bredo Greve for several years before studying at the Royal Danish Academy of Art while also assisting Martin Nyrop with his designs for Copenhagen City Hall.
He is most commonly associated with his restoration designs for Nidaros Cathedral in Trondheim, Norway. Nordhagen returned to Oslo in 1906 and accepted a number of smaller commissions. Nordhagen designed a number of industrial structures, notably Såheim in Rjukan (with Thorvald Astrup).
Designed several churches. And completed considerable research around Norwegian traditional architecture. Dating from 1913, he was also a professor at the Norwegian Institute of Technology in Trondheim.
Olaf Nordhagen is probably most famous for the restoration designs of the Nidaros Cathedral. He took over project management of this work upon the death of Christian Christie and carried it through until his own death in 1925. His tendency to reinterpret Gothic designs rather than seek a faithful reproduction of the original was controversial at the time but was carried out.