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.
David Cameron has said there is an “economic, moral and practical” case for lower taxes as he set out his central election pledges on taxation.
The prime minister said, under his plans, no-one would pay tax on the first £12,500 of their income by 2020.
In a speech in Hampshire, he said the government had a track record of taking the lowest-paid out of tax altogether.
But Nick Clegg said it was a “brazen attempt” by the Conservatives to take credit for a Liberal Democrat policy.
The Conservative-Lib Dem coalition has increased the point at which people start paying income tax – known as the annual personal allowance – from £6,475 in 2010-2011 to £10,500 in 2014, meaning those earning less than £100,000 now pay no tax on the first £10,500 of income.
Both parties have pledged to lift this threshold to £12,500 during the next Parliament although they are at odds over who has spearheaded the policy, with both seeking to take the credit.
Top Ugandan rebel commander Dominic Ongwen has appeared in the dock at the International Criminal Court (ICC) in The Hague to face war crimes charges.
Mr Ongwen, a feared commander of the Lord’s Resistance Army (LRA), is the first member of the LRA to appear before the court.
During the pre-trial hearing he was asked to confirm his identity.
He faces charges of crimes against humanity and war crimes, including murder and enslavement.
The LRA is accused of seizing children to use as fighters and sex slaves.
The prosecution is not expected to formally put its case for some time.
Mr Ongwen wore a blue suit, white shirt and chequered tie in court. He identified himself as born in Gulu in northern Uganda in 1975.
“I was abducted in 1988 and I was taken to the bush when I was 14 years old,” he said in Acholi, the language widely spoken in northern Uganda. “Prior to my arrival at court I was a soldier in the LRA.”
Mr Ongwen was arrested after giving himself up in the Central African Republic last month. Last week he was delivered to the ICC.
His transfer “brings us one step closer to ending the LRA’s reign of terror”, ICC chief prosecutor Fatou Bensouda said in a statement last week.