Sergio Mattarella, 73, will be backed by Renzi's ruling Democratic Party (PD) in a parliamentary selection procedure expected to produce a new head of state by Saturday, the premier said ahead of a first round of voting.
Renzi's declaration of support was unanimously approved by PD lawmakers in a show of hands. That is no guarantee that all of them will actually cast their secret ballots for Mattarella, which was reflected in Renzi's appeal for party discipline.
"If the PD gives a name, we stake our credibility on that candidate," he said. "There will not be another PD candidate."
Matterella, now a member of Renzi's broad church centre-left party, is a former Christian Democrat from Sicily who entered parliament after his elder brother, Piersanti, then the island's regional president, was assasinated by the mafia in 1980.
Previously a legal academic, Mattarella has served in several ministerial roles in both centre-right and centre-left governments, including stints as education and defence minister. White-haired and bespectacled, he has been a constitutional judge since 2011.
The president is selected by an electoral college of 1,009 politicians: the members of the Chamber of Deputies and the upper-house Senate are joined by 58 representatives of the regions.
A two-thirds majority is required to produce a winner on the first three rounds of voting. A simple majority, or 505 votes, is sufficient in the fourth. Renzi's PD has 415 members in the college.