Letta, from the Democratic Party (PD), said he would start talks to form a broad-based coalition on Thursday. It is likely to go to parliament for a vote of confidence by early next week.
The prime minister designate is expected to select a group of ministers, likely to be a mixture of politicians and technocrats, under the guidance of Napolitano, whose own unprecedented re-election last weekend opened the way for an end to the crisis.
The new government will be backed primarily by Letta's centre-left and the centre-right People of Freedom party (PDL) led by Silvio Berlusconi, which had previously failed to reach a deal following inconclusive elections two months ago.
Rivalries between the parties as well as rifts within the PD, which fell short of a viable parliamentary majority in February's vote, could still block an accord. But formation of a government after such a long impasse would signal that Italy is finally ready to make a start on much-needed reforms.
Accepting his mandate, Letta said he would not form a government "at all costs", warning that the warring parties must make compromises or he would withdraw.
He said Italy faced an untenable situation and the government must provide answers on jobs, poverty and the crisis facing small businesses in a recession that now matches the longest since World War II.
Criticism for EU policies
European Union economic policies had been too focused on austerity instead of growth, he said, and Italy's parliamentary system must be reformed together with the widely criticised electoral law that has virtually guaranteed stalemate.
The bespectacled and balding Letta is an urbane moderate who speaks fluent English and at 46 would be one of Italy's youngest prime ministers, representing a generational change from the era of Berlusconi and outgoing Prime Minister Mario Monti.
A staunch pro-European and a member of the now-defunct Christian Democrat party in his youth, he is likely to be welcomed by foreign governments and markets and can also work with the centre-right.
He is the nephew of Berlusconi's longtime chief of staff, Gianni Letta, and has numerous political friends on all sides of parliament, which could help ease the fractious climate since the election.
As Letta met close aides, the names being circulated as likely future ministers suggested a government broadly in line with Monti's outgoing technocrat administration but including senior politicians such as PDL party secretary Angelino Alfano.
Bank of Italy director general Fabrizio Saccomanni was seen as a possible economy minister and Enrico Giovannini, head of statistics agency ISTAT, may take over the industry ministry. Monti himself could return as foreign minister, helping to maintain the international contacts he cultivated as premier.
