According to both Landnámabók and Íslendingabók, Celtic monks known as the Papar lived in Iceland before Scandinavian settlers arrived, possibly members of a Hiberno-Scottish mission. Recent archaeological excavations have revealed the ruins of a cabin in Hafnir on the Reykjanes peninsula. Carbon dating indicates that it was abandoned sometime between 770 and 880. In 2016, archeologists uncovered a longhouse in Stöðvarfjörður that has been dated to as early as the year 800.

Swedish Viking explorer Garðar Svavarsson was the first to circumnavigate Iceland in 870 and establish that it was an island. He stayed over winter and built a house in Húsavík. Garðar departed the following summer but one of his men, Náttfari, decided to stay behind with two slaves. Náttfari settled in what is now known as Náttfaravík and he and his slaves became the first permanent residents of Iceland.

The Norwegian-Norse chieftain Ingólfr Arnarson built his homestead in present-day Reykjavík in the year 874. Ingólfr was followed by many other emigrant settlers, largely Scandinavians and their thralls, many of whom were Irish or Scottish. By 930, most arable land on the island had been claimed; the Althing, a legislative and judicial assembly, was initiated to regulate the Icelandic Commonwealth. Lack of arable land also served impetus to the settlement of Greenland starting in 986. The period of these early settlements coincided with the Medieval Warm Period, when temperatures were similar to those of the early 20th century. At this time, about 25% of Iceland was covered with forest, compared to 1% in the present day. Christianity was adopted by consensus around 999–1000, although Norse paganism persisted among some segments of the population for some years afterwards.