Mr Hollande capitalised on Mr Sarkozy's unpopularitySocialist Francois Hollande has been elected as France's new president, early estimates say.
He got about 52% of votes in Sunday's run-off, according to projections based on partial results, against 48% for centre-right incumbent Nicolas Sarkozy.
Mr Hollande would be the first French socialist president since 1995.
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.
The estimates were carried by French media after all polling stations closed at 20:00 (18:00 GMT).
Exuberant Hollande supporters have already converged on Place de la Bastille in Paris - a traditional rallying point of the Left - to celebrate.
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 also wants to raise the minimum wage, hire 60,000 more teachers and lower the retirement age from 62 to 60 for some workers.
Mr Sarkozy, who has been in office since 2007, had promised to reduce France's large budget deficit through budget cuts.
It is only the second time an incumbent president fails to win re-election since the start of France Fifth Republic in 1958.
The last was Valery Giscard d'Estaing - he was beaten in 1981 by socialist Francois Mitterrand, who had two terms in office until 1995.
The new president is expected to be inaugurated later this month.
A parliamentary election is due in June.
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