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.
Mr Sarkozy, who has been in office since 2007, urged his UMP party to remain united, but warned he would not lead it into June's parliamentary elections, according to AFP news agency.
It quotes him as telling party leaders, as he read a draft of his concession speech: "Stay together. We must win the battle of the legislatives. I will not lead that campaign."
It is only the second time an incumbent president has failed to win re-election since the start of France's 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.
Perhaps now the US Fed can get the Europeans to do what we did and throw trillions more at the problem. The Japanese have been doing this as well for the last couple of decades, though not as 'whole hog' as we have in so short a time frame, but then that's expected of a vassal state subject to the whims of 'big brother' and his desire to weaken his currency.
This increase in the money supply is the classic means of dealing with a sluggish economy, but it won't solve the main problem, but then all they have to do is keep 'kicking the can down the road' a little longer until it's time to say, 'Goodnight Irene'. Mr. H will have lots of company in thinking and doing so, especially if they do it the 'American Way', off the books, out of sight as usual.