Crowds gathered to celebrate in Athens as results began to come through
With two-thirds of ballots counted, results from the Greek referendum show voters decisively rejecting the terms of an international bailout.
Figures published by the interior ministry showed 61% of those whose ballots had been counted voting "No", against 39% voting "Yes".
Greece's governing Syriza party campaigned for a "No", saying the bailout terms were humiliating.
The "Yes" campaign warned this could see Greece ejected from the eurozone.
Some European officials had also said that a "No" would be seen as an outright rejection of talks with creditors.
But Greek government officials have insisted that a "No" vote would strengthen their hand and that they could rapidly strike a deal for fresh funding in resumed negotiations.
Greek banks will reopen by Tuesday, they say.
Reacting to the result, Greek Finance Minister Yanis Varoufakis called it "a big yes to a democratic Europe".
He said Greece would be "positive" in negotiations with its creditors.
Euclid Tsakalotos, Greece's deputy foreign minister, told Star TV that two developments would allow Greece to pursue "a solution that is financially viable".
"Firstly, the government now has a new popular mandate and the second is the latest [International Monetary Fund] report which says that the Greek debt is unsustainable."
Greece had been locked in negotiations with its creditors for months when the Greek government unexpectedly called a referendum on the terms it was being offered.
Banks have been shut and capital controls in place since last Monday, after the European Central Bank declined to give Greece more emergency funding.
Withdrawals at cash machines have been limited to €60 per day.
The partying by the "No" camp will go well into the night here and the government will be popping open the ouzo. Alexis Tsipras has called the eurozone's bluff - and it appears to have gone his way.
But the triumphalism won't last. There is still a sizeable chunk of the Greek nation deeply unhappy with what has happened. And the government will have to unite a divided country.
More than that, a deal with the eurozone has to be struck fast.
Greek banks are running critically low and will need another injection of emergency funds from the European Central Bank.
Given the bad blood of the past two weeks - Greece's Finance Minister, Yanis Varoufakis, calling the eurozone's strategy "terrorism" - it will be hard to get back around the negotiating table. And with the banking crisis and tax revenues plummeting amidst the instability, Greece's economy has weakened again, making a deal even harder to reach.
The eurozone's tough rhetoric will continue. But Greece's government will have its answer prepared: we put your demands to a democratic test - and they were rejected.
Mr Varoufakis is due to meet senior Greek bankers later on Sunday. State Minister Nikos Pappas, a close ally of Prime Minister Alexis Tsipras, said it was "absolutely necessary" to restore liquidity to the banks now the referendum was over.
Italian Foreign Minister Paolo Gentiloni tweeted: "Now it is right to start trying for an agreement again. But there is no escape from the Greek labyrinth with a Europe that's weak and isn't growing."
Belgium's finance minister said the door remained open to restart talks with Greece "literally, within hours".
Eurozone finance ministers could again discuss measures "that can put the Greek economy back on track and give the Greeks a perspective for the future," he told the VRT network.
French President Francois Hollande and German Chancellor Angela Merkel are scheduled to meet in Paris on Monday to discuss the situation, Mr Hollande's office said.
Greece's latest bailout expired on Tuesday and Greece missed a €1.6bn (£1.1bn) payment to the IMF.
The European Commission - one of the "troika" of creditors along with the IMF and the European Central Bank - wanted Athens to raise taxes and slash welfare spending to meet its debt obligations.
Greece's Syriza-led government, which was elected in January on an anti-austerity platform, said it had been presented with an "ultimatum".
The Greek government's opponents and some Greek voters had complained that the question on the ballot paper was unclear. EU officials said it applied to the terms of an offer that was no longer on the table.
The projected turnout in Sunday's referendum was about 60%.