The lighthouse on the eastern part of the promontory was built in 1916 and rebuilt in 1948 and at the same time a radio beacon for the international flights was installed. The Danish consul, Dithlev Thomsen, had the rescue hut for shipwrecked people built there in 1912. The promontory was named after the first Norwegian settler of the country. He and his foster-brother Hjorleifur had undertaken an expedition to Iceland a few years earlier to acquaint themselves with the country. They spent one winter in the East and sailed back to Norway to prepare for their emigration. When they came back with their families and belongings their ships drifted apart off the south coast. Ingolfur landed by the promontory and made his winter lodgings there. Hjorleifur found another promontory, Hjorleifshofdi, further west and spent the next winter there.
Ingolfshofdi lighthouse is on the Saga trail for South Iceland.