Letta asked to lead Italy
The appointment of 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 has left the country in flux.
In a statement, Letta said as prime minister 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.
The 46-year-old also said he had accepted the post knowing that it was an enormous responsibility and that Italy’s political class “has lost all credibility”.
Letta must now form a cabinet that can win cross-party support and a vote of confidence in parliament.
Factions from across the political spectrum have indicated that they are now ready to form a coalition under a figure like Letta.
He is the nephew of former Prime Minister Silvio Berlusconi’s chief-of-staff Gianni Letta, and is seen as a moderate acceptable to the centre-right.
A broad alliance would include Berlusconi’s right-wing group – making him again a major political 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, says the BBC’s Alan Johnston in Rome.
But it is a forced political marriage that may not last long, our correspondent adds.
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. (BBC)