Norðoyri is first mentioned in writing in 1584, but excavations at Islendingatoftir, a few miles south of Norðoyri have demonstrated that this place was already inhabited during the Viking Age.
Prvá písomná zmienka je z roku 1584, ale vykopávky v Islendingatoftir, niekoľko kilometrov južne od Norðoyri ukázali, že toto miesto bolo osídlené už v časoch Vikingov.