Renzi - currently still mayor of Florence and known as the "demolition man" - ousted his Democratic Party (PD) colleague late Thursday after he called for "radical change" in an economically stagnant and politically unstable Italy.
"If we don't take risks and we don't take responsibility now, the slow pace of reform, without a strong push on our behalf, could result in losing our economic competitiveness," Renzi said at Thursday's party meeting.
(Read More: Italy's Letta to submit resignation Friday)
President Napolitano said Friday that he would complete consultations with the center-left PD party officers by Saturday and is expected to give a mandate to Renzi to form a new government. If Renzi accepts, he will then face a confidence vote in both chambers of the Italian parliament.
"The takeover of Renzi is likely to be seen by the market as a moderately positive event as it would increase the likelihood of an acceleration of the reform process in Italy," Fabio Fois and Giuseppe Maraffino, two analysts at Barclays said in a research note on Thursday evening.
Renzi is seen as the brash, young leader that could seek and gain tougher reforms. He has called for political measures designed to enhance growth and job creation and streamline the bureaucracy and judiciary system. On Thursday, he stated that any new government should deliver structural and institutional reforms, which would include changing the voting system and amending the constitution.
Italy, the third-largest economy in the 18-country euro zone after Germany and France, has been struggling to get its finances in order. The country's debt as a proportion of its gross domestic product was 127 percent in 2012, according to European statistics database Eurostat. The only other euro zone country with a higher debt level is Greece at 159 percent. The country's unemployment rate remains stubbornly high at 12.7 percent.
Economists at UniCredit, Chiara Corsa and Loredana Federico, believe that the President will move rapidly to give Renzi his mandate and suggest that the PD Party leader has already been in talks with the political parties of the coalition which had previously supported Letta.
They expect Renzi to have between 170-175 votes in the Senate, with an absolute majority needed of only 161 seats out of 321.
(Read More: Italy's Letta says anyone wanting him to resign must say so)
"On balance, we see a high probability that Renzi will manage to secure a decent majority in the Senate. Things will be easier in the lower house, where, Renzi is expected to have a comfortable majority," the UniCredit economists said in a note on Thursday evening.
"The risk of early elections will diminish a lot. This is positive news, since going to the polls now – before the approval of a new electoral law that replaces the current proportional system – would most likely lead to a hung parliament."
As well as a new leader, Italy received yet more good news on Friday morning with gross domestic product for the country posting a moderate quarterly gain of 0.1 percent, the first time Italy has posted growth in almost three years.