Papademos, 64, The former European Central Bank vice-president, was named as Greece’s new prime minister, following days of negotiations.
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.
Papademos is not a member of parliament, but will head an interim government until elections can take place in February.
The people of Greece hope his instalment will provide the stability to get them through the country’s debt crisis.
“The job will not be easy, but I am convinced the problems will be solved … in a quicker and more efficient way if there is unity and consensus,” the new prime minister said.
 The govermment’s main task will to ensure Greece, which is laden with debt, gets its latest bailout payment by approving a new £111bn international rescue package from eurozone partners and the International Monetary Fund.
The Greek president’s office said in a statement: “The president, after recommendations by political leaders who attended the meeting, has instructed Lucas Papademos to form a new government.”
The new government will be sworn in at 12:00 GMT on Friday, a presidency official said.
Papademos said the first priorities of the transitional government were to ratify the bailout agreed at an EU summit last month, and to implement the policies linked to it.
That will involve another round of austerity measures, which have already proved hugely unpopular with the Greek public.
Papademos replaces Greece’s outgoing Prime Minister, George Papandreou, who was forced to step down after unsuccessfully calling for a referendum on the eurozone rescue package.
The suggestion sparked a wider financial and political crisis.
The new prime minister faces a confidence vote in parliament on Monday, Greek state TV reported.
His appointment led to a sharp rise in the Greek stock market.
Meanwhile, in Italy, there was increasing speculation that former European Commissioner Mario Monti would take over from outgoing Prime Minister Silvio Berlusconi.The markets appeared to calm amid hopes that the economist would take over the reins shortly, correspondents say, and borrowing levels fell back from the previous day’s record highs.