Antonis Samaras has vowed to "give hope" to the Greek people, moments after being sworn in as prime minister.
His party, New Democracy, has forged a coalition with the Socialists (Pasok) and the smaller Democratic Left.
The deal ends weeks of uncertainty in Greece. An inconclusive election on 6 May raised fears Greece could leave the eurozone and trigger a wider crisis.
But the new coalition is expected to face immediate pressure from an austerity-weary Greek public.
They have endured five years of recession and are increasingly resistant to the tough terms of Greece's huge bailout from the EU and International Monetary Fund (IMF).
Syriza - the leftist party that came second in Sunday's poll and strongly opposes the austerity measures - will be a defiant voice of opposition, correspondents say.
Greek stocks rose moderately in response to the news that a coalition had been formed, with Athens shares closing up 0.5%.
'Burden of responsibility'
Mr Samaras became Greece's fourth prime minister in eight months at a brief ceremony at the presidential palace in Athens, presided over by the archbishop of Greece and chanting Orthodox Greek clergy.
In his first public words following his swearing in, he asked the Greek people for "patriotism and strong national unity and trust, [so] that with the help of God, we'll do whatever we can for the people to come out of this crisis".
The 61-year-old said he would demand "hard work" from the new government "so that it will be able to give hope to our people".
The three coalition party leaders are due to meet outgoing Finance Minister Giorgos Zanias and the man tipped to be his successor, National Bank chairman Vassilis Rapanos, on Wednesday evening.
More detail on the cabinet make-up is also expected to emerge before Thursday, when Mr Zanias will represent the new government at a meeting of eurozone finance ministers in Luxembourg.
Earlier, announcing the coalition deal, Pasok leader Evangelos Venizelos said the three parties in the new coalition had "taken on the burden of responsibility to renegotiate the bailout agreement and [the job] of exiting Greece from the crisis".
Democratic Left leader Fotis Kouvelis said he expected the cabinet to "release the country from the painful terms" of the bailout, reported AFP news agency.
The BBC's Andrew Walker in Brussels says European leaders will be relieved that there is now a Greek government to negotiate with, but concern about what they will be asking for.
European leaders have indicated that there is limited room for manoeuvre on the bailout.
Greece has seen many street demonstrations - sometimes violent - by people angered by the job losses, pay cuts and reduced welfare resulting from the bailout.
The country got an initial EU-IMF package worth 110bn euros (£89bn; $138bn) in 2010, then a follow-up this year worth 130bn euros.
It has also had 107bn euros (£86bn; $135bn) of debt, held by private investors, written off.
New Democracy won 129 seats in Greece's 300-seat parliament on Sunday, followed by Syriza with 71, Pasok with 33 and the Democratic Left with 17.
Between them, New Democracy, Pasok and Democratic Left would have a majority of 29.