He was born in Decorah, Iowa in the United States as a son of vicar Karl Anton Fjellbu (1865–1933) and his wife Ellen Johanne Retvedt (1865–1941).

[1] In April 1940 the occupation of Norway by Nazi Germany started, supported by the Norwegian political party Nasjonal Samling.

[1] On 1 February 1942, however, the authorities demanded that Nazi priest P. Blessing-Dahle preside over the church ceremony to celebrate the inauguration (Norwegian: statsakten) of the Quisling regime.

[1] Fjellbu had a son, also named Arne (born 1921), who was imprisoned in Falstad concentration camp from 9 March to 9 June 1942.

He stayed in Finnmark until late March, when he was called to London to speak at a memorial sermon in Westminster Abbey on 9 April.

He returned from the United Kingdom to Stockholm by plane on 1 May 1945, heading for Finnmark, but due to the events instead travelled to Trondheim by train, arriving on 9 May, and conducting a sermon in a crowded Nidaros Cathedral the following day.

[1] During the war years, Fjellbu documented events in a secret diary, parts of which were published as Minner fra krigsårene in 1945.