Results published by the interior ministry showed about 60% of those whose ballots had been counted voting “No”, against some 40% 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.
Senior 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.
“The mandate from the Greek people is for the government to defend its own proposal and its own positions,” government spokesperson Gabriel Sakellaridis said as results began to come in on Sunday. “The real negotiations must start from tonight.”
‘New popular mandate’
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.