Greece has lurched into uncharted territory and an uncertain Eurozone future after voters overwhelmingly rejected demands by international creditors for more austerity measures in exchange for a bailout of its bankrupt economy.
Results showed 61pc voted No compared with 39pc for Yes.
Greek finance minister Yanis Varoufakis resigned after the ballot, saying his decision was made to further the Greek people's cause.
"We of the left know how to act collectively with no care for the privileges of office," said Mr Varoufakis, who had become a focal point for friction in meetings with Greece's international creditors.
He hailed the No vote in the referendum as a victory for democracy that would have global impact.
"The superhuman effort to honour the brave people of Greece and the famous 'oxi' ('no') that they granted to democrats the world over is just beginning," he said this morning.
He added that prime minister Alexis Tsipras had judged that his resignation "might help achieve a deal" and that he was leaving the finance ministry for this reason.
Mr Varoufakis is known for his brash style and had visibly annoyed many of the Eurozone's finance ministers during Greece's debt negotiations.
He said the prime minister had judged it "potentially helpful to him" if he is absent from the upcoming meetings with Greece's creditors.
"I shall wear the creditors' loathing with pride," he said.
The referendum, Greece's first in more than 40 years, came amid severe restrictions on financial transactions in the country, imposed last week to stem a bank run.
Thousands of jubilant government supporters celebrated in Athens' Syntagma Square in front of parliament.
It was a decisive victory for Mr Tsipras, who had gambled the future of his five-month-old coalition government and his country in an all-or-nothing game of brinkmanship with Greece's creditors from other European countries that use the euro, the International Monetary Fund (IMF) and the European Central Bank (ECB).
"Today we celebrate the victory of democracy," Mr Tsipras said in a televised address to the nation, saying it was "a bright day in the history of Europe".
"We proved even in the most difficult circumstances that democracy won't be subjected to blackmail," he said.
Mr Tsipras called the referendum last weekend, saying a No vote would strengthen his hand to negotiate a better deal for his country. His government has said it believes it would be possible to conclude a deal with creditors within 48 hours.
But European officials and most of Greece's opposition parties painted the referendum as one of whether the country kept using the euro, even though that was not the convoluted question asked on the ballot.
"Given the unfavourable conditions last week, you have made a very brave choice," Mr Tsipras told Greeks in his address. "But I am aware that the mandate you gave me is not a mandate for rupture."
German chancellor Angela Merkel and French president Francois Hollande spoke last night and agreed "the vote of the Greek people must be respected", Mrs Merkel's office said.
Time has run out for Greece. The international bailout - under which the country received nearly €240bn in rescue loans - expired last week, on the same day Greece defaulted on an IMF repayment, becoming the first developed nation to do so.
Of critical importance will be whether the ECB decides to maintain its lifeline to Greece in the form of emergency liquidity assistance. That assistance, now at around €90bn, has been maintained but not increased in past days.
Yesterday's vote was held after a week of capital controls imposed to halt a bank run, with Greeks restricted to a daily cash withdrawal of €60.
Long lines have formed at ATMs, while pensioners without bank cards have thronged the few bank branches opened to allow them access to a maximum €120 for the week.
Some analysts say Greece is so starved of cash that it could be forced to start issuing its own currency.