The appointment of Enrico Letta, currently deputy leader of the centre-left Democratic Party, could see the end of two months of parliamentary deadlock.
An inconclusive general election in February left the country in political limbo.
Enrico Letta, 46, said he would aim to change the course in Europe on austerity.
“European policies are too focused on austerity which is no longer enough,” he said, following the closed-door meeting with the president in Rome.
He also said he had accepted the post knowing that it was an enormous responsibility and that Italy’s political class “has lost all credibility”.
Enrico Letta must now form a cabinet that can win cross-party support and a vote of confidence in parliament, possibly this weekend.
Factions from across the political spectrum, including former PM Silvio Berlusconi’s right-wing People of Freedom Party (PDL), have indicated that they are ready to form a coalition under a figure like Enrico Letta.
However, Silvio Berlusconi’s party and the Democratic Party (PD) differ on a number of issues.
PDL National Secretary Angelino Alfano warned that his group would not take part in a government unconditionally.
Enrico Letta, once a member of the former centre-right Christian Democrats, is seen as moderate of the left. His uncle, Gianni Letta, has been Silvio Berlusconi’s chief-of-staff for 10 years.
A broad political alliance would again make Silvio Berlusconi a major influence.
This awkward coming together of bitter rivals is seen as the only way to end the parliamentary stalemate and put an administration in place.
But it is a forced political marriage that may not last long.
Enrico Letta’s candidacy for prime minister came about after the PD leader, Pier Luigi Bersani, announced his resignation last week.
He had ruled out working with Silvio Berlusconi and faced a party rebellion over his choice for Italian president.
The third strongest political force to come out of February’s election, former comedian Beppe Grillo’s Five Star movement, could not be persuaded to join a coalition and is expected to be in opposition.
With the Italian economy still struggling, the new government will be expected to try to implement a limited range of economic and institutional reforms.
Among its priorities will be an effort to re-shape the current election law. The aim would be to ensure that future general elections would deliver more emphatic, clear-cut results.
Enrico Letta’s appointment follows the swearing-in on Monday of President Giorgio Napolitano, who berated his country’s feuding politicians.
Taking up an unprecedented second term, he told the assembled MPs that they had been guilty of a long series of failings and that their inability to implement key reforms had been “unforgivable”.
Giorgio Napolitano has threatened to resign if no administration is formed.
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