How can a non-EU citizen move to Iceland?
A non-EEA citizen needs a residence permit granted before travelling, usually based on a specific job offer, a study place, or a family member already living here. Útlendingastofnun decides the application, and arriving first and applying later is the mistake that costs people the most time.
The permit type decides everything that follows: how long you may stay, whether you may change employer, whether your family may come, and whether these years will later count towards permanent residence.