Emmanuel Macron and Marine Le Pen are to contest the second round of the French election on 7 May after a ballot marked by a historically high turnout believed to be close to 70%.
Macron, of the En Marche movement, took 23.7% of the vote on Sunday (23 April) while Le Pen, the leader of the far right Front National, took 21.7%.
Their success saw, for the first time in modern history, no one from the mainstream centre-right or centre-left parties making it to the second round.
Macron is the hot favourite to win the run-off with one poll putting him at 68% to 32% ahead of his rival.
At the age of 39 if he were to win he would become the youngest French president for nearly 170 years after Louis-Napoleon Bonaparte who became the country's head of state at the age of 40 in 1848.
In his victory address, Macron struck a note of unity as well as patriotism. Amid cries of "Macron, president!", he told the audience at the Parc des Expositions hall in Paris how he wanted to unite the country.
"Take the risk that is yours to join me as well as the parliamentary majority I will build right from tomorrow. We will reign. Long live the Republic! Long live France!"
Le Pen had a similarly adoring crowd which she addressed in Henin-Beaumont.
She said: "This is a historic result and now I have the immense responsibility to defend the French nation its unity, its security, its culture, its prosperity and its independence.
"At the same time it can be interpreted as an act of French confidence in the future. The French must seize this historic moment because what is at stake is wild globalisation that endangers civilisation".
The election saw the demise of the traditional French left and the French right. Socialist Francois Hollande became the first sitting president in modern history not to seek re-election.
Francois Fillon, who took 19.5% of the vote, was third. His appeal was hampered by allegations of corruption and a scandal involving expenses allegedly paid out to his family. Meanwhile, the hard-left candidate Jean-Luc Mélenchon who got a slightly smaller percentage in the vote, said he would not concede until the results were finalised.
Both Fillon and Benoît Hamon, who took 6.2% of the vote, threw their support behind Macron and urged their supporters to back him to block the ascent of Le Pen.
There were scuffles in central Paris, with reports of three arrests at the Place de la Bastille where demonstrators burned cars, danced around bonfires and dodged riot police.
Protesters have waved red flags and sung "No Marine and No Macron!" No injuries have been reported.
There has been positive reaction around Europe overMacron's performance as he shapes up to the be the favourite to win the presidency in two weeks.
Spokesman for Angela Markel, Steffan Siebert said it was "good that Emmanuel Macron has been successful with his positions for a strong EU and a social market economy. Good luck for the coming two weeks."
Germany's Social Democrats chairman, Martin Schultz, called on "all French democrats to unite so the nationalist does not become president".