Greek Prime Minister Alexis Tsipras took his oath of office a day after being re-elected in a snap general election.
Mr Tsipras took a civil oath "to uphold the constitution and laws" of the country.
He is expected to name a coalition government by Wednesday to begin applying the terms of the tough EU bailout he signed onto in July.
The EU congratulated Mr Tsipras on his left-wing party's election victory and said Greece has "no time to lose" in implementing the reforms under its international bailout.
"The commission congratulates Alexis Tsipras for his victory," European Commission spokesman Margaritis Schinas told reporters.
He recalled that under Mr Tsipras's previous leadership, Greece already "committed to ambitious programme of reforms" to revive the country's economy as he led the negotiations that culminated in the bailout deal signed in Brussels in August.
"The new government will now have the mandate to carry out those reforms... There is a lot of work ahead and no time to lose."
Mr Schinas said Greece's creditors, the EU, the European Central Bank and the International Monetary Fund were expected to meet over the next few months to conduct a review aimed at releasing new funds under the bailout deal.
With around 90% of votes counted, the Syriza party looked set to secure close to an absolute majority in the country's 300-seat parliament, with a smaller nationalist party expected to join forces and push it over the top.
The commission also welcomed what it saw as the "ample representation of pro-European parties" in parliament that are committed to a strong Greece within the 19-country Eurozone, Mr Schinas said.
He added that Commission President Jean-Claude Juncker has already written to Mr Tsipras and will talk to him later in the day.
Mr Tsipras's far-left party secured 35.5% of the vote, well ahead of its nearest rival New Democracy, which won just over 28%.
Speaking to jubilant supporters last night, Mr Tsipras said that Greeks were now synonymous with dignity and struggle, but he warned of difficult times ahead.
It was a resounding and surprising victory. Mr Tsipras took a risk after 25 members of his party split over the bailout he signed up to, and it has paid off.
Party officials were nervous before the result that a low turnout and a sense of betrayal among core supporters could mean a narrow defeat.
However, the electorate appeared to keep their faith in Mr Tsipras, although Syriza will have a smaller majority than before, even as it accepts the Independent Greeks as its coalition partner.
In contrast to his ebullient predictions back in January, when he promised to end bailouts and austerity, Mr Tsipras tempered his victory speech with a reminder that there are tough times ahead.
He directed his rhetoric not against the eurozone or bailouts but against what he called the old corrupt ways of the Greek political system.
In words which could have been written by the country's creditors Mr Tsipras said recovery would not come magically but through hard work.
The result is likely to be welcomed in eurozone capitals since Syriza now has a mandate to implement the painful reforms that come with the third bailout, but many within the party are still deeply opposed to those reforms.
