Lucas Papademos called for the nation to unite and to be optimistic about the future. ( Image: BBC )
Leaders of the three main parties making up a new government of national unity had been meeting the Greek president to try to reach a deal.
The new Prime Minister will also face a confidence vote in parliament, which is expected to happen on Monday.
Mr Papademos, who is not a member of parliament, will head an interim government until elections can take place in February 2012.
Greeks hope the news will provide the stability to get them through their debt crisis.
A presidency official said the new government will be sworn in at 12:00 GMT today.
The exact framework of the new coalition government is yet to be agreed.