While Iceland is not a member of EU, it participates in the EU Single Market through its membership of the European Economic Area. One consequence of that is that freedom of movement for workers applies to Iceland and Icelanders in the same way as to the EU proper.
An EU citizen has the right to live and work in Iceland indefinitely without prior permission (but must register with civil authorities within 6 months, like native Icelanders have to). The rules also give quite liberal rights to move to Iceland to seek work on your own expense for up to six months.
The Icelandic government informs about the procedure at https://www.skra.is/english/individuals/moving-to-iceland/