The opposition accused Tsipras of jeopardising the country's membership in the 19-nation club that uses the euro and said a "yes" vote was about keeping the common currency.
With 87 per cent of the votes counted, the "no" side had more than 60 per cent.
"Today we celebrate the victory of democracy," Tsipras, who gambled the future of his 5-month-old left-wing government on the vote, said in an address to the nation.
On Sunday night's result, he said that "'no' is a big 'yes' to democratic Europe. It's a no to the vision of Europe an infinite cage for its people. It is a loud yes to the vision of the Eurozone as a common area of prosperity and social justice."
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Thousands of government supporters gathered in central Athens in celebration, waving Greek flags and chanting "No, No, No."
Governing left-wing Syriza party Eurodeputy Dimitris Papadimoulis said that "Greek people are proving they want to remain in Europe" as equal members "and not as a debt colony."
The referendum was Greece's first in 41 years.
Minister of State Nikos Papas, speaking on Alpha television, said it would be "wrong to link a 'no' result to an exit from the eurozone. If a 'no' prevails that will help us get a better agreement."
"Today, democracy is defeating fear ... I am very optimistic," Tsipras said earlier in the day after voting in in Athens.