ROME — Italy’s victorious anti-establishment forces declared a new epoch of their country’s political life Monday, hours after an election demolition of the traditional parties that dominated the nation for decades.

Both the surging populist 5-Star Movement and the anti-migrant far-right League party claimed a win after Italians cleared their rivals and left them as the most potent forces in the country. The shift all but guarantees an anti-establishment leader for Italy and was a powerful display of Italians’ fury with old-line politicians and with the European Union in Brussels.

Luigi Di Maio, the 5-Star leader, compared the day to other monumental moments in Italian history when the old political order was swept out the door.

“Today, for us, the third republic commences,” Di Maio said. “At last, the republic of Italian citizens.”

With 99 percent of the vote counted on Monday evening, the traditional center-left and center-right parties combined had managed to beat 5-Star’s 32.6 percent vote total by only a sliver of a percentage point — an extraordinary collapse for them and a confirmation of the new populist power.

And well over half of Italians voted for EU-skeptic parties that have questioned Italy’s use of the euro currency and its alliance with the West against Russia. The League, whose leader Matteo Salvini last year signed an agreement with the political party founded by Russian President Vladimir Putin, claimed its own victory on Monday with 17.4 percent of the vote. They now stand astride a center-right coalition, which received 37 percent of the vote, and in which they had been forecast as junior partners.

“I see this as a vote for the future,” Salvini told supporters on Monday. “I am and will remain a populist, one of those who listens to the people and does their duty.”

Analysts said that even as the results were messy, the combined power of the anti-system candidates pointed to one clear victor: anger.

“There are two sides of this common root: rage and of rebellion against the political elites,” said Massimiliano Panarari, who teaches politics at Rome’s LUISS University.

With the shattered landscape leaving no single force with a clear route to power, it remained unclear on Monday whether the 5-Star Movement or the League would get the first chance at trying to form a coalition. Either is likely to make Europe’s establishment nauseous. If Salvini came to power, he would be Western Europe’s first far-right leader since 1945. Di Maio, meanwhile, questions European integration and rules that restrict free spending. The two parties could also ally with each other since they share many views about the economy. But many analysts say a coalition is unlikely because 5-Star’s left-wing voters might be repelled by the League’s anti-migrant stances.

The choice of which party gets the first chance to form a government will be made by Italian President Sergio Mattarella. Many here expect the haggling will last months.