The far-left Syriza party, which won Greece's general election on Sunday, has formed an anti-austerity governing coalition with the right-wing party Greek Independents.
The coalition will have a comfortable majority in Greece's new parliament.
Syriza leader Alexis Tsipras has vowed to renegotiate Greece's bailout, worth €240bn (£179bn; $268bn), to end Greece's "humiliation and pain".
Several European politicians have warned him to respect bailout terms.
The euro recovered from an 11-year low against the US dollar as investors digested what Syriza's victory means for the eurozone's future.
Savouring victory: the leader of an anti-austerity revolution
Europe's main share markets also rose - after initial falls - on hopes that a compromise over Greece's bailout terms might be found.
With nearly all of the votes counted in Sunday's poll, Syriza looks set to have 149 seats, just two short of an absolute majority. The Greek Independents are projected to have 13 seats in the 300-seat parliament.
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The election result is expected to be one of the main issues at Monday's meeting of 19 eurozone finance ministers.
Sunday's result means that a majority of voters in Greece have essentially rejected a core policy for dealing with the eurozone crisis as devised by Brussels and Germany, the BBC's Gavin Hewitt in Athens says.
The troika of lenders that bailed out Greece - the European Union, European Central Bank, and International Monetary Fund - imposed big budgetary cuts and restructuring in return for the bailout money.
But the man tipped to become the new Greek finance minister Yanis Varoufakis, told the BBC the austerity regime had been "fiscal waterboarding policies that have turned Greece into a debt colony".
The economy has shrunk drastically since the 2008 global financial crisis, and increasing unemployment has thrown many Greeks into poverty.
Syriza leader Alexis Tsipras: "Today the people of Greece wrote history"
On Sunday, Mr Tsipras told jubilant supporters: "Your mandate is undoubtedly cancelling the bailouts of austerity and destruction.
"The troika for Greece is the thing of the past," he added.
Mr Tsipras promised to write off half of Greece's debt, but was ready to negotiate "a viable solution" and wants the country to stay in the eurozone.
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