If you are a Nordic national from Denmark (including the Faroe Islands, Greenland and the Åland Islands), Finland, Norway or Sweden you should go to the following page: I am a Nordic national
A residence permit is required for citizens outside the EEA/EFTA area who intend to reside in Iceland for more than three months. The Icelandic Directorate of Immigration decides whether residence permits are issued. Further information can be found on The Directorate of Immigration website or at their reception at Dalvegur 18, 201 Kópavogur.