Ms Sigurdardottir said Icelanders had called for a "change of ethics"
Iceland's interim centre-left government has won a resounding victory in early parliamentary elections.
The coalition secured 34 seats in the 63-member parliament - an increase of seven MPs from the previous election.
Iceland's centre-right government resigned in January amid mass street protests following the country's economic collapse.
Prime Minister Johanna Sigurdardottir says her priority will be to start negotiations with the European Union.
The Social Democratic Alliance and the Left Green Movement formed a coalition caretaker government in February, under Ms Sigurdardottir.
We lost this time but we will win again later
Independence Party leader
Ms Sigurdardottir said the results of Saturday's poll were "historic".
"This is the first time that leftist parties will hold a majority," she said
She told supporters the nation was "settling the score with the neoliberalism" and with the conservative Independence Party who "have been in power for much too long".
"The people are calling for a change of ethics. That is why they have voted for us," she said.
The Independence party, which secured 16 seats, conceded defeat after its worst election results in decades.
Its new leader Bjarni Benediktsson said it was clear that his party had lost the trust of voters.
"We lost this time but we will win again later," he said.
Professor Olafur Hardarson of the University of Iceland said the elections were also historic for other reasons - it resulted on both the highest number of first time MPs - 27 in total - and the highest number of women in parliament since voting began in Iceland in 1874.
The economic crisis led to widespread public anger
The two coalition parties will now have to reach an agreement on how to move forward with a European Union application.
Pro-EU Ms Sigurdardottir said it was her priority to start negotiations with the Union to see what deal the country could reach - which would then be put to the nation in a referendum.
However, the Left Green Movement - the other coalition partner - remains eurosceptic.
The small North Atlantic nation has a population of only 300,000.
It had to take a $10bn (£6.8bn) rescue package, led by the International Monetary Fund, after its banking sector imploded late last year.