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 now turn 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 June legislative elections — the next challenge for Sarkozy's conservatives.
"The hour is one of mobilization. ... We must not give all the power to the left," said Jean-Francois Cope, leader of Sarkozy's UMP party.
The Socialists will have blanket control of the country if they get a majority in the decisive lower house of parliament. They already preside over the Senate and hold most regions and municipalities in France.
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.
Hollande wants to modify one of Sarkozy's key reforms, over the retirement age, to allow some people to retire at 60 instead of 62. He wants to hire more teachers and increase spending in a range of sectors, and ease France off its dependence on nuclear energy. He also favors legalizing euthanasia and gay marriage.
Sarkozy supporters call those proposals misguided.
"We're going to call France the new Greece," said Laetitia Barone, 19. "Hollande is now very dangerous."
Sarkozy had said he would quit politics if he lost, but was vague about his plans Sunday night.
"You can count on me to defend these ideas, convictions," he said, "but my place cannot be the same."
Sarkozy alienated many voters with a lunge to the right during the last two weeks of campaigning as he tried to lure backers of the far-right anti-EU and anti-immigration candidate Marine Le Pen, leader of the National Front party.
People of all ages and ethnicities celebrated Hollande's victory at the Bastille. Ghylaine Lambrecht, 60, who celebrated the 1981 victory of Mitterrand, was among them.
"I'm so happy. We had to put up with Sarko for 10 years," she said, referring to Sarkozy's time as interior and finance minister and five years as president. "In the last few years, the rich have been getting richer. Now long live France, an open, democratic France."
"It's magic!" proclaimed Violaine Chenais, 19. "I think Francois Hollande is not perfect, but it's clear France thinks it's time to give the left a chance. This means real hope for France. We're going to celebrate with drink and hopefully some dancing."
Jamey Keaten in Tulle, France, and Elaine Ganley, Sarah DiLorenzo, Thomas Adamson, Greg Keller, Sylvie Corbet and Cecile Brisson in Paris contributed to this report.