Hollande led conservative incumbent Nicolas Sarkozy by 51.3% to 48.7% with 83% of votes counted, the Interior Ministry said, bringing the centre-left back to government in Paris after a decade in opposition.
"Europe is watching us," the president-elect said in a victory speech in his constituency of Tulle in central France.
"I'm sure that in many European countries there is relief and hope at the idea that austerity does not have to be our only fate," Hollande said in remarks apparently aimed at German Chancellor Angela Merkel.
Franco-German relation reshaped
The election comes at a crucial time for the eurozone as France, Europe's No. 2 economy, is a vital partner for Berlin.
Hollande's clear win should give the self-styled "Mr Normal" the momentum to press Merkel to accept a policy shift towards fostering growth in Europe to balance the austerity that has fuelled anger across southern Europe.
Merkel, who had openly favoured fellow conservative Sarkozy, telephoned to congratulate Hollande and invited him to visit Berlin as soon as possible after his inauguration next week.
German Foreign Minister Guido Westerwelle, speaking at French embassy event, said: "We will now work together on a growth pact for Europe, that delivers more growth through more competitiveness."
In his victory speech, Hollande listed "reorienting Europe towards employment and growth" as among his top priorities.
He has made clear he will not to force a ground-up review of the EU's fiscal pact, driven by Merkel and Sarkozy earlier this year, and aides say there will be give and take with Berlin.
Merkel's camp says she is not opposed to his proposal to give the European Investment Bank a more active financing role and making better use of structural funds but she is sceptical on his idea of common EU project bonds to fund infrastructure.
Merkel herself spent an uncomfortable evening as her centre-right Christian Democrats looked likely to lose further local power after a state election in Schleswig-Holstein, continuing a pattern that may erode her chances of a third term next year.
Vote ends 'Merkozy' duo
The vote put an end to the "Merkozy" duo which had led Europe through crisis and ushers in a new, untested partnership.
Voters ousted incumbent President Nicolas Sarkozy for failing to rein in unemployment, becoming the 11th euro zone leader in succession to be swept from power since the currency bloc's debt crisis began in 2009.
The outgoing president conceded defeat within 20 minutes of polls closing, telling supporters he had telephoned Hollande to wish him good luck in such trying times.
"I bear the full responsibility for this defeat," Sarkozy said, indicating he would withdraw from frontline politics.
"My place can no longer be the same. My involvement in the life of my country will be different from now on."