As with the Faroes, legend has it that a few Irish monks already lived in Iceland prior to the Vikings’ arrival. This is certainly plausible, especially since it seems that the Norse already knew of Iceland’s existence prior to their first trip there. In any case, if they were there before the Norse arrived, they left soon after, presumably because they didn’t want their hallowed solitude disrupted – especially not by pagans.
The first Viking party to Iceland set foot on its shores in about 860. It was exploratory in nature, and no one stayed around to settle. The island was given its name by a member of that party named Floki (Flóki Vilgerðarson), who was dismayed by the harshness of the winter.
Norse settlement of Iceland began in about 870. Around half of the settlers seem to have come from the region of Norway around Bergen, with their chief motivation having been to escape the draconian rule of King Harald Fairhair. The other half came from other parts of Scandinavia and the British Isles. By 920 or 930, all of the land suitable for farming had been settled, and by the middle of the tenth century, Iceland had tens of thousands of inhabitants.
The original population of Iceland seems to have had a significant Celtic admixture, so a number of Celts must have accompanied the Vikings as spouses, slaves, or in some other capacity. There were Christians among the original settlers, and the proportion of Christianity relative to paganism increased over time, with the official conversion around the year 1000 being a watershed year in the process.
Although Iceland remained a free state for centuries, Norway exerted a significant cultural and political influence over it, surely due to the significant number of Norwegians amongst the early settlers. In the mid-thirteenth century, well after the end of the Viking Age, Iceland formally submitted to Norwegian rule.