Archeologists have a precise method for dating the settlement of Iceland.
A volcano eruption occurred right around A.D. 871, and covered much of southwestern Iceland
with a layer of ash. Any objects found below this layer would date to
before A.D. 870, whereas objects found above this layer date to after
that period. So far, no archeological remains or sites have been found
predating the ash layer, suggesting that the settlement of Iceland was
a Viking activity, without prior Celtic involvement.
While sagas and the historical evidence suggest a degree (usually estimated at 30%) of Celtic participation in the settlement of Iceland, probably as slaves of Viking chieftains, the archeological evidence such as Viking Age houses and material remains indicates the settlement was overwhelmingly a Norse activity.
Several objects from the few pagan/Viking burials do indicate that the
earliest inhabitants of Iceland had cultural ties to many areas, including
Saami-land, Sweden, and Finland. Most of the non-Viking objects
are from the Western Isles. This includes jet, which is mined only at
the English town of Whitby, and ringed-pins, which were made in Dublin
and exported throughout the North Sea. Though not conclusively identifying
the ethnicity of the person, these objects certainly suggest ties with
areas outside of the Scandinavian homelands, especially the Western Isles.
Studies of Viking houses provide the best information about the Viking settlement of Iceland and the Faeroes. Excavations of Viking Age longhalls, like the one at the farm of Erik the Red, reveal that these houses are all remarkably similar to Viking houses in Norway: a long rectangular house with slightly curved walls, a few internal partitions, a slab-lined central hearth in the largest room, and an entrance near the end of one of the lateral walls.
Does a Viking style house mean the builders were Scandinavian? Housing styles are almost always unique to a culture. In some places, such as in the Orkneys, there is a sudden shift in housing types from round Pictish houses to rectangular Viking houses in the late 9th century. The replacement of a local tradition suggests either a violent military takeover, or a change of cultural traditions through contact. Regardless of the cause, changes in housing style are conclusive archeological evidence for a new cultural presence. In Iceland and the Faeroes, no Pictish or other Celtic style houses have ever been found.
In both the Faeroes and Iceland, there are numerous place-names which are partially comprised of the word 'papar', meaning priest. Based on Dicuil's report from about A.D. 825, many have assumed these place-names are the areas where Irish monks were living at the time that the Vikings first arrived. However, archeological investigations at these sites have found no structures of Celtic design, no Celtic artifacts, and no Christian burials. If papar were in Iceland before the Vikings, they left no archeological traces.