New PM appointed amid calls for early elections later in the year, after Panama Papers led previous leader to step down.
Icelanders have elected historian Gudni Johannesson as their first new president in 20 years.
The final count showed 39 percent of Icelanders voted for him, placing him in front of a former prime minister and central bank governor.
The post is largely ceremonial but does carry powers to block legislation.
The political newcomer ran for presidency amid distrust of politicians and business leaders after the 2008 global financial crisis and the Panama papers scandal.
In his campaign, Johannesson advocated a constitutional clause allowing citizen-initiated referendums over parliamentary bills, saying it would help ensure the nation always had the final say in the largest issues affecting it.
Iceland had expected a low voter turnout as the election was eclipsed by the country’s eagerly-anticipated Euro football match.
The interior ministry had even set up a polling station in France near the national football team’s camp in Annecy, where fans have followed their team into the knockout stage of the championship.
In the end, more people than expected turned out with preliminary figures saying 185,000 out of 245,000 of those eligible to vote made it to polling stations.
Johannesson, 47, an expert on political history, diplomacy and the constitution came to prominence in April as a public commentator on the case of former prime minister Sigmundur David Gunnlaugsson, who resigned over leaked data in the Panama Papers suggesting he and his wife had an offshore company in the British Virgin Islands.
His first day in office will be August 1, when he succeeds Olafur Ragnar Grimsson, who did not want to stand again after 20 years and five terms in office.
Iceland has been gradually recovering from the 2008 financial meltdown in recent years. Economic growth is expected to reach 4 percent this year and unemployment is at a pre-crisis levels.
But gross national income per capita is still down by a quarter since 2007 and a tenth of the 330,000 Icelanders have fallen into serious loan default, with thousands of homes repossessed.