He will take office no later than May 16.
Sarkozy is the latest victim of a wave of voter anger over spending cuts in Europe that has ousted governments and leaders in the past couple of years.
Hollande portrayed himself as a vehicle for change across Europe. "In all the capitals . . . there are people who, thanks to us, are hoping, are looking to us, and want to finish with austerity," he told exuberant crowds of supporters in a speech early Monday at Paris' Place de la Bastille. "You are a movement lifting up everywhere in Europe, and perhaps the world."
The party lasted into the night on the iconic plaza of the French Revolution, with revelers waving all kinds of flags and climbing the base of its central column. Leftists are overjoyed to have one of their own in power for the first time since Socialist Francois Mitterrand was president from 1981 to 1995.
"Too many divisions, too many wounds, too many breakdowns and divides have separated our fellow citizens. This is over now," Hollande said in his victory speech, alluding to the divisive Sarkozy presidency. "The foremost duty of the president of the Republic is to unite . . . in order to face the challenges that await us."
Those challenges are legion, and begin with Europe's debt crisis.
Hollande has said his first act after the election will be to write a letter to other European leaders calling for a renegotiation of a budget-trimming treaty aimed at bringing the continent's economies closer together. Hollande wants to allow for government-funded stimulus programs in hopes of restarting growth, arguing that debts will only get worse if Europe's economies don't start growing again.
Sarkozy and Germany's Angela Merkel spearheaded the cost-cutting treaty, and many have worried over potential conflict within the Franco-German "couple" that underpins Europe's postwar unity.
Merkel called Hollande to congratulate him on his victory. Hollande has said his first trip would be to Berlin. Merkel's foreign minister joined calls for a growth pact - but one that doesn't necessarily require more spending.
Hollande will also head soon to the United States for summits of NATO - where he will announce he is pulling French troops out of Afghanistan by the end of the year - and the Group of Eight leading world economies.
While some market players have worried about a Hollande presidency, Jeffrey Bergstrand, professor of finance at the University of Notre Dame, said it's a good thing that Hollande will push for more spending throughout Europe to stimulate the economy.
Europe is "going into a really serious and poor situation." Hollande "is going to become the speaker for those countries that want to do something about economic growth," Bergstrand said.
Sarkozy conceded defeat minutes after the polls closed, saying he had called Hollande to wish him "good luck" as the country's new leader.
"I bear responsibility . . . for the defeat," he said. "I committed myself totally, fully, but I didn't succeed in convincing a majority of the French. . . . I didn't succeed in making the values we share win."
Sarkozy came to office on a wave of hope for change that critics say he squandered even before the economic crises hit. They saw his tax reforms as too friendly to the rich, his divorce in office and courtship of supermodel Carla Bruni as unseemly, and his sharp tongue as unfitting for his esteemed role.
French politicians turned their attention to parliamentary elections next month. With what appears to be a thin victory margin, Hollande must more than ever count on a healthy majority in legislative elections - the next challenge for Sarkozy's conservatives.
Hollande has pledged to tax the very rich at 75 percent of their income, an idea that proved wildly popular among the majority of people who don't make nearly that much. But the measure would bring in only a relatively small amount to the budget, and tax lawyers say France's taxes have always been high and unpredictable and that this may not be as much of a shock as it sounds.