With Greece due to run out of money in a few weeks, the European Union told bickering political parties to explain by Monday evening how they would form a unity government to get the 130-billion-euro ($180-billion) emergency funding.
Papandreou, who sealed his fate last week with a disastrous 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 Papandreou and conservative leader Antonis Samaras came up with the bare minimum to satisfy Brussels, and they must still agree on Monday who will become the next prime minister to lead a nation that is destabilizing the entire euro zone.
A former deputy president of the European Central Bank, Lucas Papademos, is the front runner to become the new prime minister, Greek media said on Monday.
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 hold a confidence vote within a week, if all went to plan.
"Finally!" the center-left daily Ta Nea said on its front page on Monday. "The first, big step has been taken to save the country." Conservative daily Kathimerini wrote: "A first win."
Others were less charitable. "I'm afraid the new government will very soon turn out to be problematic," said Stefanos Manos, a conservative formerfinance minister.
On the streets of Athens, many Greeks, who have suffered pay and pension cuts and massive job losses in the past two years, remained skeptical.
"Are we saved? I don't think so if nothing is done to stop this practice of slapping more and more taxes because people's pockets will be empty," said Nikos Stratakis, 49, a taxi driver.
"Hurrah, we are saved!" George Vihos, a plumber, said sarcastically. "Weren't we the ones who did not want these austerity measures? Why should we celebrate now that they will make sure we bear the pain."
A SUITABLE DATE
The new coalition must win parliamentary approval for the bailout before calling early elections.
Papandreou's socialist PASOK party and the New Democracy party of Samaras agreed early on Monday that the most suitable date for the elections would be February 19 next year.
Brussels has piled pressure on Athens to approve the bailout, a last financial lifeline for Greece, fearing that its crisis will spill into much bigger euro zone economies such as Italy and Spain -- which would be far harder to rescue.
Papandreou and Samaras had been scrambling to reach a deal before finance ministers of euro countries meet in Brussels on Monday evening, to show that Greece is serious about taking steps needed to stave off bankruptcy.
Earlier, European Economic and Monetary Affairs Commissioner Olli Rehn told Reuters that finance ministers from countries that use the single currency would insist on hearing a plan for a unity government from their Greek colleague Evangelos Venizelos at Monday's Eurogroup meeting.
"We have called for a national unity government and remain persuaded that it is the convincing way of restoring confidence and meeting the commitments," he told Reuters. "We need a convincing report on this by Finance Minister Venizelos tomorrow in the Eurogroup."
Papandreou had sought the referendum to show that harsh cuts demanded in the bailout had public support, but the risk that a "no" vote could bring about a sudden bankruptcy caused mayhem in markets and unrest in the ruling party.
He soon ditched the idea and won a confidence vote in parliament, but only after promising to make way for the national unity coalition.
BACK SEAT DRIVING
The coalition deal is unlikely to calm Greek politics.
Whoever becomes prime minister will struggle to exert their authority as the party leaders run things behind the scenes, Manos told Reuters. "The civil service won't implement any decision and everyone will be waiting for the election."
Papandreou and Samaras -- who were once college room mates in the United States -- had to bury their deep differences and personal animosity, as Greece is deep in economic, political and social crisis, its future in the euro zone is in question, and their reputations among ordinary Greeks are at rock bottom.
"The two leaders had no other choice. If elections were held now, nobody would turn out to vote for them," said Elias Nikolakopoulos, political science professor at Athens University.
Papandreou and Samaras are due to discuss on the phone on Monday morning who will be the new prime minister.
The favorite, Papademos, was vice president of the European Central Bank from 2002-10. As a former governor of the Bank of Greece in 1994-2002, he oversaw the country's efforts to join the euro zone.
President Papoulias, who led the talks that produced Sunday's deal, will summon the head of all leading parties for more negotiations at 1800 GMT on Monday.