Hollande, who was expected to confirm the move in an address to the nation at 1800 GMT, decided to axe current Prime Minister Jean-Marc Ayrault after his Socialist Party lost more than 150 towns and cities to the main opposition and far-right in municipal elections yesterday.
Officials at the prime minister's official residence, Matignon, confirmed that Ayrault and the government he headed had resigned.
Waking up to headlines that included "A rout", "A slap" and "A kick up the backside", Hollande was left with little option but to order a radical shake-up of his deeply unpopular government, which is seen by many voters as drifting hopelessly in the face of a stagnant economy, persistently high unemployment and falling living standards for many people.
The scale of the setback was unprecedented.
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Marine Le Pen's FN, skilfully rebranded as more than just an anti-immigrant party, won control of 11 towns and more than 1,200 municipal seats nationwide, easily its best ever performance at the grassroots level of French government.
But even more worrying for Hollande and Co. Was the strong showing of the mainstream Union for a Popular Movement (UMP). The party of former president Nicolas Sarkozy snatched a string of major towns that were once considered bastions of the left in a performance which, if repeated in national elections, would see them sweep back to power with ease in 2017.
"This first test for Francois Hollande has been a veritable catastrophe. The Socialists' gains from the last municipals in 2008 have been completely wiped out," said Frederic Dabi of the Ifop polling institute.
UMP leader Jean-Francois Cope hailed as historic a "blue wave" that saw 155 towns of more than 9,000 residents switch from the left.