The far-left Syriza party, the winner of Greece’s election, has formed an anti-austerity coalition with a right-wing party, the Greek Independents.
The coalition will have a comfortable majority in the new parliament.
Syriza leader Alexis Tsipras has vowed to renegotiate Greece’s bailouts, worth €240bn (£179bn; $268bn).
European Commission head Jean-Claude Juncker congratulated Mr Tsipras while reminding him of the challenge of “ensuring fiscal responsibility”.
“The European Commission stands ready to continue assisting Greece in achieving these goals,” Mr Juncker said in a tweet which also referred to “promoting sustainable jobs and growth”.
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.
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.
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.