Confirmation of Papademos's role came from the Greek president's office.
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.
Greeks will hope the news will provide the stability to get them through their debt crisis, correspondents say.
Papademos will head an interim government being formed to make sure debt-strapped Greece gets its latest bailout payment, and to approve a new 130bn euro ($177bn; £111bn) international rescue package from eurozone partners and the International Monetary Fund.
"The president, after recommendations by political leaders who attended the meeting, has instructed Lucas Papademos to form a new government," the president's office said in a statement after talks between political leaders and Papademos.
The new government will be sworn in at 12:00 GMT on Friday, a presidency official said.
Papademos will replace Greece's outgoing prime minister George Papandreou who announced he was resigning after a disastrous call for a referendum on the eurozone rescue package.
The Greek stock market jumped sharply when Papademos arrived at the presidential palace to join the negotiations on Thursday morning.
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