Johannesson's Progressive Party is the biggest casualty of elections in Iceland, losing 11 of the 19 seats it held in the 63-seat parliament.
Iceland's Prime Minister Sigurour Ingi Johannsson said on Sunday he would hand the president his resignation so that a new government can be formed.
The announcement comes after an election that produced big gains for the radical Pirates but gave the largest bloc of seats to the center-right Independence Party.
Gunnlaugsson's Progressive Party was the election's biggest casualty, losing 11 of the 19 seats it held in the 63-seat parliament, as voters punished it for its links to the financial crash and corruption claims.
Saturday's election was called after then-prime minister Sigmundur David Gunnlaugsson resigned in April during public protests over his offshore holdings, revealed in the Panama Papers leak.
The conservative Independence Party took 29 percent of the vote and 21 of 63 parliament seats. Leader Bjarni Benediktsson said the party should be given a mandate by President Gudni Th. Johannesson to form a new coalition government.
The Pirates — anti-authoritarian advocates of direct democracy and digital freedom — almost tripled their vote share from 5 percent in 2013 to 14.5 percent, and will get 10 seats in Iceland's parliament, the Althingi.
The Left-Green movement, with 15.9 percent, will also get 10 seats in a parliament that is shaping up to be evenly split between parties of the left and the right.
The result was better than expected for the Independents, who have governed in coalition since 2013.
The Pirates' result fell short of what some polls had suggested — and what the party's fleet of energetic volunteers and supporters had hoped.
Like Spain's Podemos or the movement behind Bernie Sanders in the US presidential race, the four-year-old Pirates Party drew in throngs of young supporters who ran the Pirates' largely volunteer-driven campaign.
Pirates won 10 seats in Parliament. I won one of them. Epic success! There are a lot of coalition possibilities; lots of work ahead.— Smri McCarthy (@smarimc) October 30, 2016
While the conservative Independence Party made gains, "it is not a return to the status quo," said Andres Jonsson, a political consultant. To form a government, the party will have to extend its hand to smaller, more rebellious groups, he said.
"The traditional party system has been disrupted," Jonsson said. "We are not seeing big movements of people who feel that they are able to relate with the messages of the big coalition parties. Changes are going to come from the outside, not from inside the old parties."
Meanwhile, the Pirates have pledged to enhance direct democracy by passing the world's first "crowd-sourced constitution," drafted by Icelandic civilians rather than politicians. Parliament blocked the document in 2013.
About 40 percent of Pirate supporters are under the age of 30. They had pinned their hopes on a party that has promised to instal a more inclusive and transparent government.
The election was dominated by Iceland's economy — now recovering on the back of a tourism boom, with low unemployment and high growth — and voters' desire for political reform.
Iceland's Pirate Party, founded four years ago by an assortment of hackers, political activists and Internet freedom advocates, campaigned on promises to introduce direct democracy, subject the workings of government to more scrutiny and place the country's natural resources under public ownership.
The party also backs tough rules to protect individuals from online intrusion. Birgitta Jonsdottir, the Pirates' most senior lawmaker is a former ally of WikiLeaks who has called on Iceland to offer citizenship to US National Security Agency leaker Edward Snowden.
Opponents argued that the inexperienced Pirates could scare off investors and destabilise the economy — a message that resonated with some voters.
Jonsdottir said she was satisfied with the result. "Whatever happens, we have created a wave of change in the Icelandic society," she told a cheering crowd early Sunday.