He got about 52% of votes in Sunday’s run-off, according to early projections, against 48% for centre-right incumbent Nicolas Sarkozy.
Mr Sarkozy has admitted defeat, saying: “Francois Hollande is the president of France and he must be respected.”
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.
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.