Since the budget law has been approved he (Renzi) offered the resignation of the government over which he presides.
Renzi was set to present his resignation on Monday after the decision.
Populists in Italy and throughout Europe rejoiced at Renzi's downfall, in the wake of anti-establishment poll shocks in both Britain and the United States.
After staking his political reputation on a controversial referendum, the prime minister has acknowledged defeat and tendered his resignation. It was a sharp retort to Renzi's characterizing the reforms as an opportunity to shrink the "caste" of elite, perk-enjoying politicians by reducing the numbers and powers of Senators.
One of the proposed reforms would have stripped the Senate of most of its powers and make it no longer directly elected. But his gamble backfired as it turned the referendum into a vote on his record in office. Italian President Sergio Mattarella told Italian premier Matteo Ren.
He had promised to wait until the Senate passed the 2017 budget, which it did earlier in the day.
Earlier in the afternoon, Renzi had gathered the leadership of his center-left Democratic Party (PD), which is the largest in parliament, to outline its political strategy for the government crisis. But markets rebounded as European officials dismissed talk of a broader euro zone crisis.
Renzi addressed his Democratic Party (PD) before meeting the president, saying the party would only participate in a government meant to last until 2018 if it was backed by all the main forces in parliament, a prospect which seems remote. Party leaders are due to meet on Wednesday.
Opinion polls show the PD is neck-and-neck with 5-Star, which wants to hold a referendum on membership of the euro.
The former three-time premier has said he would vote "No".
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The populist 5-Star Movement says it's poised to govern Italy now that Premier Matteo Renzi is resigning. The size of the "No" vote, at 59.1 percent, was more emphatic than had been forecast.
Mattarella asked Renzi to carry on in a caretaker capacity while he consults with the political parties about next steps, the President's office said in a statement.
The referendum verdict sent the European single currency crashing to $1.0506 - the lowest level since mid-March 2015 - before bouncing back over $1.07.
By early in the European morning, the currency had largely rebounded.
On Wednesday, a Treasury spokesman denied Italy was poised to ask for a loan from the European Stability Mechanism to support its banking sector.
In New Zealand, the NZX 50 lost grown after Prime Minister John Key said he would resign.
"We want to go to the ballot box soon", said Roberto Fico, a 5-Star lawmaker. And in Italy, like elsewhere, anti-establishment parties are banging at the doors of government.
"For Italy, establishing stable governance and a plan to guide the nation is of critical importance given the fragility of the economy, challenging policies and the liquidity problems in the banking system".
Norbert Hofer, who was seeking to become the first far-right president in Europe since the Second World War was beaten by the Green Party's Alexander Van der Bellen.
But elsewhere, the established order is in retreat. French President Francois Hollande announced last week he would not seek re-election next year and even German Chancellor Angela Merkel looks vulnerable as she seeks a fourth term in 2017.