Francois Fillon oversaw Nicolas Sarkozy's election campaign
Mr Fillon, 53, a moderate conservative senator, helped direct Mr Sarkozy's successful election campaign.
He is expected to play a leading role in the president's plans to reform France's employment and welfare laws.
Mr Sarkozy, who succeeded Jacques Chirac on Wednesday, is due to name the rest of his government on Friday.
He has promised to halve the number of government ministers to 15, and has said about half will be women.
The outgoing prime minister, Dominique de Villepin, who resigned from the post on Tuesday, received his successor and formally handed over power in a ceremony on Thursday morning.
FRANCOIS FILLON Nicolas Sarkozy's election campaign director and jogging partner A senator, from the left of Mr Sarkozy's conservative UMP party Has a Welsh wife, Penelope, and five children
Profile: Francois Fillon
In line with tradition, the Republican Guard was deployed in ceremonial uniform and Mr Fillon arrived via a red carpet laid out across the courtyard at the prime minister's official residence, the Matignon.
During the ceremony the new prime minister said: "I will listen to everyone because a France in motion needs everyone."
Afterwards Mr de Villepin emerged from the Matignon, wished Mr Fillon good luck and said: "He has all the necessary qualities to succeed in the service of our country."
Mr Fillon served as social affairs minister between 2002 to 2004, pushing through a major overhaul of the country's pension system in the midst of large street protests.
He has also served in several other government posts for the UMP party, but lost his place in Mr Chirac's administration in 2005 and pledged his loyalty to Mr Sarkozy.
Reform agenda
The new president said on his first day in office that France needed to bring in more reforms quickly.
Getting France moving again - Mr Sarkozy sets the pace
"There is a demand for change. Never have the risks of inertia been so great for France as they are now in this world in flux where everyone across the world is trying to change quicker than the others, where any delay can be fatal," he said.
Shortly afterwards, the pair put on their jogging kits and went for a brisk run around the Bois de Boulogne.
The BBC's Caroline Wyatt, in Paris, says all this is a new and very different style for France, whose heads of state here have traditionally been patrician, somewhat remote figures.
It is clear that Mr Sarkozy and Mr Fillon are serious about getting this nation moving again, she says, beginning by setting their own personal example.
Mr Fillon's renowned conciliatory skills will be much needed as prime minister if he is to succeed in a post often described as a poisoned chalice, says the BBC's Alasdair Sandford in Paris.
Mr Fillon will lead the UMP party into parliamentary elections in June.
Opinion polls suggest the party will gain a majority, giving Mr Sarkozy and Mr Fillon the scope to push ahead with reforms.
The new President of France, Nicolas Sarkozy has appointed François Fillon to head the new French government. Fillon's predecessor Dominique de Villepin stepped down yesterday, and formally handed over the post during a ceremony today.

The nomination did not come as a surprise after the British newspaper the '''' had reported on May 8 that Sarkozy had introduced Fillon to Tony Blair in a telephone conversation.

François Fillon (53) has been the political advisor of Sarkozy in the  for the past 2 years, and he was Sarko's campaign leader during the recent presidential elections. Fillon has experience in negotiating with the trade unions, having undertaken controversial reforms of the  and the pension system. Sarkozy in his inauguration speech on Wednesday reiterated his plans to reform the French labour and social system, and Fillon will have to oversee these reforms as the new Prime Minister. Sarkozy said he wants to make the economy more flexible and lessen social tensions.


'''' reported that Fillon is an Anglophile; his wife Penelope Clarke, with whom he has 5 children, was born in Wales. Ideologically, Fillon is being described as a moderate left-leaning member of the conservative UMP party.

Fillon had his first experience as a minister in 1993 when he became Minister for the Higher education and Research under PM . He later became Minister for the Post office, Telecommunications and Space, then Minister for the social Affairs, Work and Solidarity, and finally Minister for national Education, the Higher education and Research. At the university, he studied public law and political sciences.

Sarkozy might announce his cabinet of 15 ministers as early as Friday, half of which are going to be women, he said. Fillon will lead the UMP in the parliamentary elections next month. A poll on Wednesday predicted a 1.5% increase in votes for the UMP, up to 40%, compared to 28% status-quo for the allied socialists.

Reports say that Sarkozy has offered the foreign minister post to , co-founder of , who is seen as being on the left in French politics.