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.
Syriza leader Alexis Tsipras has taken the oath as the new prime minister.
He 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 BBC’s full coverage of the reaction can be found here.
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.
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.
On Sunday, Mr Tsipras told jubilant supporters he wanted 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.
Analysis: Robert Peston, BBC Economics Editor
If Syriza were to win its negotiations with the rest of the eurozone, other anti-austerity parties would look more credible to voters. The victory of protectionist Marine le Pen in France’s presidential election would be an interesting test of markets’ sangfroid.
And if Syriza were to lose in talks with Brussels and Berlin, and the final rupture of Greece from the euro were to take place, investors might well pull their savings from any eurozone country where nationalists are in the ascendant.
So why are investors not in a state of frenzied panic? Why have the euro and stock markets bounced a bit this morning? One slightly implausible explanation is that investors believe the eurozone would actually be stronger without Greece, so long as no other big country followed it out the door.
More likely is that they believe reason will prevail, and Berlin will sanction a write-off of Greece’s excessive debts.
Arriving for the meeting in Brussels, the chairman of the Eurogroup, Jeroen Dijsselbloem, told reporters: “There is very little support for a write-off in Europe.
“The most important thing is that if you remain in the eurozone you stick to the rules we have.”
Mr Dijsselbloem said the possibility of a further extension of the bailout – which runs out at the end of February – was on the agenda of the Eurogroup meeting.
German Chancellor Angela Merkel’s spokesman also said Greece had to stick to its previous commitments.
Belgian Finance Minister Johan Van Overtveld was quoted by VRT network as saying that Greece “must respect the rules of monetary union”, although he added that there was room for some flexibility.
UK Chancellor of the Exchequer (finance minister) George Osborne told the BBC Syriza’s promises would be “very difficult to deliver, and incompatible with what the eurozone currently demands”.
Italy’s EU Affairs Minister Sandro Gozi sounded a more positive note, speaking of “new opportunities to pursue change in Europe to create growth and investment and fight against unemployment”.
New Greek Coalition – Allies And Dates To Watch
- Syriza, acronym meaning the “Radical Coalition of the Left”, was formed in 2004 and is led by Alexis Tsipras, 40; first came to prominence after 2008 Greek riots
- The Greek Independents, a right-wing party formed as a New Democracy splinter in 2012 and led by Panos Kammenos; hard line on immigration
- Both allies want to end austerity and renegotiate Greece’s debt
- 26 Jan: Alexis Tsipras is sworn in as prime minister
- 27 Jan: Government cabinet expected to be named
- 28 Feb: Bailout extension expires
- 20 Jul: 3.5bn euro bonds mature