Napolitano will begin consultations on Friday with political leaders to pick a nominee to replace Letta, which the presidency said would conclude on Saturday.
Letta was forced to announce his resignation on Thursday after his own Democratic Party (PD) overwhelmingly backed a motion by its new leader Renzi calling for a new government.
On Friday Letta "submitted the irrevocable resignation of the executive that he presides," the presidency said.
It added that Napolitano would move swiftly to find an "efficient solution" to the political crisis and move on with economic and "urgent" election law reforms.
The outgoing premier smiled as he arrived at the presidential palace and thanked his supporters in a tweet after losing in the showdown with Renzi.
"Thank you to everyone who helped," said Letta, a 47-year-old former Christian-Democrat who had defiantly ruled out resigning and presented his programme of reforms for 2014 as recently as Wednesday.
Al #Quirinale a rassegnare le dimissioni al Capo dello Stato.Grazie a tutti quelli che mi hanno aiutato."Ogni giorno come se fosse l'ultimo"
— Enrico Letta (@EnricoLetta) February 14, 2014
The "relay" between Letta and Renzi is unpopular among Italians who would have preferred early elections, according to opinion polls, and there is concern in the party that it could end up strengthening disgraced former prime minister Silvio Berlusconi.
Pippo Civati, a leftist opponent of Renzi within the party, said the ambitious leader was resembling more and more "a character from a roman noir novel".
Analysts said Renzi will have to overcome the shock caused by him engineering Letta's overthrow despite an earlier gentleman's agreement that he would not do so.
But they also said he could quickly win support if he manages to push through important reforms, and investors were broadly supportive with stocks and bond rates holding stable on the financial markets.
"The reform process will probably get a boost," Italy's UniCredit bank said in a research note, adding however that "the road ahead is not without bumps".
Stocks on Friday jumped up 1.6 percent as Letta resigned, also thanks to new data showing that the economy grew by 0.1 percent in the fourth quarter.
The result was the first positive one for gross domestic product in two years after Italy's longest post-war recession ended in the third quarter.