The excitement has been building for two weeks, it was mixed with relief and perhaps some disbelief when the first estimate was broadcast. They have waited 17 years for a Socialist president.
More than 350 polls published since the beginning of this campaign said he would win - still they cannot quite believe it. President Hollande: "It still takes some getting used to," said Senator Helene Conway-Mouret. "A year ago you would never have dreamed it."
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. And he was officially announced as the new French President shrtly before the outgoing President - Sarkozy went on air to concede defeat.
Exuberant Hollande supporters gathered on Place de la Bastille in Paris - a traditional rallying point of the Left - to celebrate.
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.
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.
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