Italy's prime minister, Enrico Letta, will step down on Friday after the leadership of his centre-left party deserted him for Matteo Renzi – a telegenic and smooth-talking rival who cites Tony Blair as a role model and now looks likely to become the country's youngest premier in modern history.

At the conclusion of a power struggle between the two Democratic party (PD) heavyweights, Letta issued a statement on Thursday night saying he would tender his resignation to President Giorgio Napolitano on Friday at the Quirinale palace.

Minutes before, the PD's national committee had voted by 136 votes to 16, with two abstentions, to back a motion put forward by Renzi, the party leader and mayor of Florence, calling for a new government capable of opening "a new phase" of reform and pulling the eurozone's third-largest economy "out of the quagmire".

While it did not directly refer to Renzi, there was no doubt who the party would be backing as Letta's successor. Although the outcome is not certain, Renzi, aged just 39, is now expected to be asked by 88-year-old Napolitano to form a new government without Italy returning to the polls for the second time in as many years.

In doing so, the man nicknamed Il Rottamatore – "the scrapper" – who has built up a substantial fan base by rejecting so-called "old politics" and its backroom deals, would become Italy's third prime minister in less than three years to take power without having been voted in.

As much as his many supporters wanted to see him eventually take power, a staffetta – or relay-race – with Letta was not the way in which they expected him to do it.

In a speech to the PD leadership, Renzi acknowledged that there were problems inherent in the strategy, describing it as "a difficult choice" full of risk. But, he said, an election now, under the country's existing electoral laws – which helped create deadlock following last year's vote – would be pointless. And the risk of forming a new administration would be worthwhile if it led to one that could last until 2018 and drive through the constitutional, electoral and bureaucratic reforms the country needed, he argued.

"This is not a matter of a relay or a non-relay. A relay is when you go in the same direction and at the same speed, not when you try to change the speed," he said.

Many had accused him of excessive ambition, he noted, but added: "Today we have to have a huge ambition, which is to think that Italy cannot exist for the coming months and coming years in a situation of uncertainty, instability, quagmire, hesitation."

Struggling to emerge from its worst post-war recession, Italy has near-record levels of unemployment, with more than 41% of young people out of work, and a public debt of more than €2tn (£1.6tn). Critics say Letta's government, which started life as an unwieldy left-right coalition with Silvio Berlusconi's PdL party and faced almost daily tensions and divisions, has been largely unable to present credible solutions.

On Wednesday evening, while – as one Italian newspaper put it – Letta was feeling the guillotine rise above him, the mild-mannered former MEP kicked back against his critics and Renzi, presenting a new agenda for reform in 2014 and defending his government's economic record, saying the country was starting to see signs of recovery.

But it was not enough to convince his opponents, or at least most of those in the PD who had until now backed him. Letta, whose high point in government arguably came in October, when he emerged victorious from a showdown with Berlusconi, stayed away from the PD meeting.

"Following the decisions taken today in the national committee of the Democratic party, I have informed the president, Giorgio Napolitano, of my desire to go to the Quirinale tomorrow to tender my resignation as prime minister," he said in his statement on Thursday night.

Almost immediately, Renzi was given a reminder of the difficulties that lie ahead in the creation of any future government when Angelino Alfano, leader of the New Centre Right (NCD) party in coalition with Letta, told journalists that if Renzi's executive did not offer the right "political conditions" for them, "we will say no to the birth of a new government".

"We are not in love with the idea of a legislature lasting until 2018," he added, saying the government would either have to do "great things" or call an election.

In turn, the Left Ecology Freedom (SEL) party that was in opposition to Letta's government but had been thought more likely to join with Renzi, made it clear it would have nothing to do with a coalition that included the NCD.

The comments appeared to underline warnings from those who see no reason why Renzi should find the same deeply divided parliament any fairer going for reform than Letta did.

"It remains to be seen whether the move will make a real difference – and there are risks involved," said Vincenzo Scarpetta of the Open Europe thinktank. "Renzi is likely to face the same political logjam which ultimately cost Letta his job, and will be exposed to fierce criticism, especially from the Five Star Movement, for being the third prime minister in a row to take power without winning an election."

Letta was parachuted into power last April after Pier Luigi Bersani, the then PD leader, failed to entice Beppe Grillo's anti-establishment movement into a coalition. Letta then formed a coalition with Berlusconi – a decision which cost him the support of many in his party.