The country's two center-right parties are projected to form a new Cabinet and then compete to name a new prime minister, the BBC reported.
Their projected victory would mark a turnaround for the conservative Independence Party and their traditional coalition partners, the Progressives. They had been blamed for the country's economic collapse in 2008. However, many Icelanders have been frustrated by austerity programs instituted by the Social Democratic Alliance in the wake of the collapse.
The center-right parties have promised debt relief and a cut in taxes.
Success by the conservatives could also end the island's attempt to join the European Union. The parties argue free-trade agreements with the EU and Iceland's inclusion in the Schengen visa-free travel zone already provide most of the benefits of full membership.
Notable deaths of 2014 [PHOTOS]