Icelandair is based in Keflavik and is a subsidiary of the Icelandair Group. It was officially founded on August 1, 1973 as a holding company between the two airlines Loftleiðir Icelandic (Icelandic Airlines) and Flugfélag Íslands (Icelandair).

Its roots, however, go back to the airline Flugfélag Akureyrar, which was founded in Akureyri on June 3, 1937. On October 1, 1979, the two airlines merged to form Icelandair.

In 2019, Icelandair had to file for insolvency at short notice and temporarily cease operations due to a slump in passenger numbers caused by the COVID-19 pandemic. After short-term renegotiations with the Icelandic government and the flight attendant company, this decision was reversed.