Francois Hollande has been elected France's first Socialist President for 17 years.
He received 52% of the vote against 48% for the incumbent Nicolas Sarkozy.
The front page of the left-leaning newspaper Liberation ran the headline "Normal!" - a reference to the new president's image as a man of the people.
The new president's honeymood period will be brief.
He is expected to be sworn in on May 15th and will travel to Berlin shortly thereafter to challenge Germany's focus on austerity policies.
Mr Hollande ran his campaign on egalitarian principles arguing against the consensus in Brussels that austerity is the way out of the Eurozone crisis.
– Francois Hollande
In every capital, beyond the heads of state and government, there are people who have found hope thanks to us, who are looking to us and want to put an end to austerity.
Today, Germany's Chancellor Angela Merkel said that she would welcome Mr Hollande's contribution to the debate, but that the fiscal pact is non-negotiable.
– Angela Merkel
We in Germany are of the opinion, and so am I personally, that the fiscal pact is not negotiable. It has been negotiated and has been signed by 25 countries. We are in the middle of a debate to which France, of course, under its new president will bring its own emphasis. But we are talking about two sides of the same coin.
ITV News' Europe Editor James Mates reports on the day after the celebrations in France.
On Sunday, Mr Sarkozy conceded defeat shortly after the polls closed, telling supporters that "Francois Hollande is the president of France" and that he was "taking responsibility for the defeat".
Hinting about his possible political future, he said he would become "a French among the French":
– Nicolas Sarkozy, outgoing French President
My place will no longer be the same. My involvement in the life of my country will now be different.
Supporters of the outgoing French president sobbed as Nicolas Sarkozy conceded defeat at the presidential elections.
Meanwhile, supporters of Francois Hollande celebrated outside Socialist Party campaign headquarters in Paris.
There were both cheers and jeers for the presidential candidates when the results were announced.