Sarkozy plans to take over power from Jacques Chirac, the outgoing president, on May 16, Fillon said, not long before France votes in parliamentary elections on June 10 and 17.
Sarkozy has promised to enact a series of tough reforms to tackle France's mounting economic and social problems.
But he will only be able to pass his proposed reforms if his UMP party retains its parliamentary majority.
Final results gave Sarkozy 53.06 per cent of Sunday's vote against 46.94 for Segolene Royal, his rival Socialist candidate.
Analysis of the results showed that Sarkozy had won critical numbers of votes in areas where he had been predicted to do relatively badly.
Around 52 per cent of women supported Nicolas Sarkozy, while only 48 per cent of women voted for Royal, according to an Ipsos poll conducted on Sunday.
In addition, some 46 per cent of blue-collar workers - traditionally leftist voters - also chose Sarkozy, according to a separate Ipsos/Dell poll.
The poll also found that 44 per cent of people of modest means voted for him, as did 32 per cent of people who usually vote for the Greens and 14 per cent who normally support the far-left.
The defeat of Segolene Royal is the third successive time that a Socialist candidate has failed to win France's presidential elections and the news has thrown the party, France's second-largest, into turmoil.
|Segolene Royal told her supporters to focus on upcoming parliamentary elections[Reuters]|
Dominique Strauss-Kahn, a leading "Blair-ite" member of the Socialist party, attacked Royal, saying that the party had failed because it had failed "to evolve into a modern left".
"The French people do not want us to offer them solutions from 20 years ago," he said.
Royal, however, brushed off the defeat and said that the party should focus on winning June's legislative elections which could allow the Socialists to block many of Sarkozy's reforms.
"We are going to work, renovate, prepare for the coming elections," she said.
"I have embarked on a renewal of political life, of its methods, and of the left."
After the results of the presidential elections were announced on Monday, supporters of Royal rioted in Paris and several other French cities including Caen and Lillie where they burnt cars and attacked shops.
Official figures released on Monday said the demonstrators had set fire to 730 cars and injured 78 policemen across France, and that 592 people were arrested in the violent protests.