Socialist Francois Hollande – who polled just under 52% of votes in Sunday’s run-off election – said he was “proud to have been capable of giving people hope again”.
Centre-right incumbent Nicolas Sarkozy is the first French president not to win a second term since 1981.
Francois Hollande has vowed to rework a deal on government debt in eurozone member countries to try and promote growth.
Admitting defeat soon after polls closed on Sunday evening, centre-right incumbent Nicolas Sarkozy wished “good luck” to Francois Hollande.
Jubilant Hollande supporters gathered at the place de la Bastille in Paris – a traditional rallying point of the Left – to celebrate.
Francois Hollande – the first Socialist to win the French presidency since Francois Mitterrand in the 1980s – earlier gave his victory speech in his stronghold of Tulle in central France.
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, Francois Hollande headed to Brive airport to fly to Paris to address supporters at the place de la Bastille.
“I am the president of the youth of France,” he told the assembled crowd of tens of thousands of supporters.
“You are a movement that is rising up throughout Europe,” he said.
Francois Hollande will begin work on forming a new government on Monday and must act quickly to reassure other eurozone countries he is up to the considerable challenge he faces.
He feeds a renewed sense of hope in the country – particularly among the young – that amid the austerity, there can be jobs and salaries, our correspondent adds. Francois Hollande offers a fresh start – but the debt problems for France are still the same
Francois Hollande has called for a renegotiation of a hard-won European treaty on budget discipline championed by German Chancellor Angela Merkel and Nicolas Sarkozy.
Angela Merkel had congratulated the president-elect by phone and invited him to Berlin to hold talks soon.
Francois Hollande’s campaign director, Pierre Moscovici, told AFP news agency that the two had agreed to work together on “a strong Franco-German relationship in the interest of Europe”.
UK Prime Minister David Cameron also called Francois Hollande to congratulate him.
Francois Hollande capitalized on France’s economic woes and President Nicolas Sarkozy’s unpopularity.
The Socialist candidate has promised to raise taxes on big corporations and people earning more than 1 million 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, Nicolas 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, Nicolas sarkozy 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.
Nicolas Sarkozy, who has been in office since 2007, had promised to reduce France’s large budget deficit through spending cuts.
He becomes the latest European leader to be voted out of office amid widespread voter anger at austerity measures triggered by the eurozone debt crisis.
Francois Hollande is expected to be inaugurated later this month. A parliamentary election is due in June.
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