Antonis Samaras, the leader of the New Democracy party, which won Sunday's election, has been sworn in as the country's new prime minister.
The ceremony came shortly after he agreed a coalition government with the Socialists (Pasok) and the smaller leftist party, the Democratic Left.
Mr Samaras took the oath at a Greek Orthodox ceremony in Athens.
He vowed his government would do whatever it could to tackle an economic crisis that has shaken the eurozone.
"Tomorrow I will ask for the new government to be formed - [we will] work hard so we can give hope to our people," Mr Samaras said.
The coalition deal follows weeks of uncertainty, after parties failed to agree a government on the results of an election on 6 May.
But the new coalition is expected to come under immediate pressure from a Greek public weary of five years of recession and increasingly resistant to the tough terms of Greece's huge bailout from the EU and International Monetary Fund (IMF).
A deal has been struck to form a new Greek coalition government, the leader of the Greek Socialists (Pasok) says.
"Greece has a government," Evangelos Venizelos said, following talks with the conservative election winner, Antonis Samaras.
Details are expected to be finalised later on Wednesday, the BBC's Mark Lowen reports from Athens.
The coalition is expected to seek some easing of the tough conditions for Greece's huge EU-IMF bailout.
Mr Venizelos said Greece would be represented by outgoing Finance Minister Giorgos Zanias at a meeting of eurozone finance ministers this week.
The small Democratic Left party is also expected to be in a ruling coalition with Pasok and Mr Samaras's New Democracy, which narrowly won Sunday's election.
Democratic Left leader Fotis Kouvelis said: "We decided to give a vote of confidence to the government that will be formed."
A New Democracy official quoted by Reuters news agency said Mr Samaras would meet President Karolos Papoulias later on Wednesday to announce the coalition deal.
New Democracy had only until Thursday to form a government, otherwise the opposition leftist bloc Syriza would get a chance. It came second in the election and strongly opposes the bailout.
Source: BBC News