French socialist Francois Hollande has won a clear victory in the country's presidential election.
Mr Hollande - who polled just under 52% of votes in Sunday's run-off - spoke of his pride at becoming president.
Admitting defeat, centre-right incumbent Nicolas Sarkozy wished "good luck" to Mr Hollande.
Analysts say the vote has wide implications for the whole eurozone. Mr Hollande has vowed to rework a deal on government debt in member countries.
Shortly after polls closed at 20:00 (18:00 GMT), French media published projections based on partial results giving Mr Hollande a lead of almost four points. Turnout was about 80%.
Jubilant Hollande supporters gathered on Place de la Bastille in Paris - a traditional rallying point of the Left - to celebrate.
People drank champagne and chanted: "Sarko, it's over!"
Mr Hollande - the first Socialist to win the French presidency since Francois Mitterrand in the 1980s - gave his victory speech in his stronghold of Tulle in central France.
He said was "proud to have been capable of giving people hope again".
He said he would push ahead with his pledge to refocus EU fiscal efforts from austerity to "growth".
"Europe is watching us, austerity can no longer be the only option," he said.
After his speech in Tulle, Mr Hollande headed to Brive airport on his way to Paris to address supporters at Place de la Bastille. His voice hoarse, he spoke of his pride at taking over the mantle of the presidency 31 years almost to the day since Socialist predecessor Francois Mitterrand was elected.
"I am the president of the youth of France," he told the assembled crowd of tens of thousands of supporters, emphasising his "pride at being president of all the republic's citizens". "You are a movement that is rising up throughout Europe," he said.
Mr Hollande has called for a renegotiation of a hard-won European treaty on budget discipline championed by German Chancellor Angela Merkel and Mr Sarkozy.
Mr Hollande's campaign director, Pierre Moscovici, told AFP news agency that Mrs Merkel had congratulated the president-elect by phone, and that the two had agreed to work together on "a strong Franco-German relationship in the interest of Europe".
Mrs Merkel later said she had invited Mr Hollande to come to Berlin soon, AFP reported.
UK Prime Minister David Cameron has also called Mr Hollande to congratulate him.
'Respect'
Mr Hollande capitalised on France's economic woes and President Sarkozy's unpopularity.
The Socialist candidate has promised to raise taxes on big corporations and people earning more than 1m euros a year.
He wants to raise the minimum wage, hire 60,000 more teachers and lower the retirement age from 62 to 60 for some workers.
In his concession speech, Mr Sarkozy told supporters: "Francois Hollande is the president of France and he must be respected."
The outgoing president said he was "taking responsibility for defeat"
Hinting about his future, he said: "My place will no longer be the same. My involvement in the life of my country will now be different."
During the campaign, he had said he would leave politics if he lost the election.
Mr Sarkozy, who has been in office since 2007, had promised to reduce France's large budget deficit through spending cuts.
He is the latest European leader to be voted out of office amid widespread voter anger at austerity measures triggered by the eurozone debt crisis.
In Greece's parliamentary election on Sunday, voters turned against the two main parties which supported tough budget cuts.
It is only the second time that an incumbent French president has failed to win re-election since the start of the Fifth Republic in 1958.
The last was Valery Giscard d'Estaing, who lost to Mr Mitterrand in 1981.
Mr Hollande is expected to be inaugurated later this month. A parliamentary election is due in June.
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