Renzi was earlier in the week asked to stay on until after the budget was passed by Italy's president Sergio Mattarella.
The 41-year-old Italian premier promised to quit if he lost the country's constitutional reform referendum on Sunday. Renzi was resoundingly defeated at the polls with 59 per cent voting against the changes.
Renzi put his political career on the line by supporting a raft of constitutional changes that included cutting the size and power of the senate.
The budget, which includes raising pension and health spending as well as preventing an increase in sales tax, was overwhelmingly passed by the Italy's lower house at the end of November and cleared its final hurdle today.
Finance Minister Pier Carlo Padoan is one of the favourite to succeed him although there has not yet been any formal announcement.
Other candidates include Senate president Pietro Grasso and transport minister Graziano Delrio.
It is also uncertain whether Renzi will continue as the leader of the Democratic Party – if he were to stay on he would likely be able to influence who takes his place.
Meanwhile, shares in Italian bank Monte dei Paschi di Siena have soared almost 10 per cent today on rumours that the Italian government is preparing a rescue bid.
According to reports, Italy will take a €2bn (£1.7bn) controlling stake in the country's third biggest bank.
The surge in the bank's shares is a turnaround from the stock's performance on Monday, when it dropped after the government lost the referendum.
The market reaction to the vote has been largely muted, with the upset somewhat priced in following shock votes in the UK's Brexit referendum and Donald Trump's election in the US.
An earlier version of this story said Renzi would resign on Friday, following Reuters' reports