Greek - 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%.