Mr Valls will be seeking the Socialist nomination for the vote, hoping to pit himself against conservative candidate Francois Fillon and Marine Le Pen, leader of the far-right Front National.
“I have appointed Mr Cazeneuve as Prime Minister and charged him with forming a new government,” said President Francois Hollande, who will not be running for re-election.
Mr Hollande said he has entrusted Mr Cazeneuve with protecting the French people.
“But protecting is not enough, we must prepare the future,” Hollande said in the Paris suburb of Villepinte.
The 53-year-old Mr Cazeneuve is a close ally of Mr Hollande and has become a popular figure in French politics as the champion of measures tackling extremism.
Since being appointed interior minister in 2014 he has led the response to a series of terror attacks which claimed more than 200 lives, championing counterterrorism and intelligence laws and implementing the country’s continuing state of emergency.
Bruno Le Roux, the head of the Socialist group in Parliament’s lower house, was appointed as France’s new interior minister.
Mr Valls, who survived a vote of no confidence earlier this year, has been criticised by members of his own party for supporting controversial labour reforms and burkini bans, and is known for his outspoken, authoritarian style and his tough views on immigration and security.
He will face other contenders in the Socialist primary next month before France’s two-part presidential election in April and May. Former economy minister Arnaud Montebourg and former education minister Benoit Hamon, who back more left-leaning policies, are also serious contenders in the Socialist primary.
An opinion poll published on Tuesday forecast that Mr Fillon would beat Ms Le Pen in the second round of the presidential election with 65 per cent of the vote.
The Ifop-Fiducial poll for iTele, Paris Match and Sud Radio also said that no candidate from the Socialist party would do better than a fifth-placed score. The survey was taken before Mr Valls put his name forward.
His party holds a majority in France’s National Assembly but its popularity has been severely damaged by the refugee crisis and the government’s inability to prevent a succession of terrorist attacks.
Additional reporting by agencies
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