With Greece due to run out of money in a few weeks, the European Union told two political parties to explain by Monday evening how they would form a unity government to enact the 130bn euro emergency funding package.
Mr Papandreou, who made an ill-fated attempt to call a referendum on the bailout, will stand down when the new government takes over, the office of the Greek president said.
But otherwise he and conservative leader Antonis Samaras came up with the bare minimum to satisfy Brussels, and they must still agree who becomes the next prime minister to lead a nation which is destabilising the entire eurozone.
Papandreou’s side trumpeted the agreement, reached late on Sunday at talks led by President Karolos Papoulias.
“Today was a historic day for Greece,” government spokesman Ilias Mossialos said, adding that the new coalition would be sworn in and would hold a confidence vote within a week, if all went to plan.