EU president Herman Van Rompuy said Draghi would succeed France's Jean-Claude Trichet as of November 1, with an eight-year mandate.
European Union leaders added that Paris had secured an extra change in the central bank's management in a delicate game of musical chairs, despite its legal independence.
|EU leaders on Friday appointed Italy's Mario Draghi, seen here on June 14|
A 63-year-old former Goldman Sachs banker, Draghi becomes the key figure at the Frankfurt-based guardian of the 12-year-old euro currency, used by hundreds of millions of citizens and businesses but facing stress on markets after governments propped up bank exposure to huge sovereign debts.
He was supposed to have been confirmed on Thursday, but was left to sweat overnight -- because Italy was already represented by Lorenzo Bini Smaghi and France, the eurozone's second largest economy, would have been left without a seat.
Van Rompuy told a news conference that Bini Smaghi had decided to quit his post early, following a gentleman's agreement between French President Nicolas Sarkozy and Italian Prime Minister Silvio Berlusconi.
Their deal could see Bini Smaghi, the unwitting focus of attention, now replace Draghi as governor of the Bank of Italy.
"I spoke on the phone this morning with Mr Smaghi," Van Rompuy said. "He indicated his intention not to see out his mandate.
"It's for Mr Smaghi to decide his timetable. We respect the (political) independence of the ECB."
A European diplomat earlier said Bini Smaghi had "committed to leave at the end of the year."
Sarkozy told journalists at the close of a two-day European Union summit in Brussels dominated by moves to offer a second, 100-billion-euro bailout to Greece over the summer, that Bini Smaghi had promised to quit within that timetable.
But analysts criticised what they said was political interference in the workings of the ECB, an institution whose independence is meant to be sacrosanct.
The eight-year mandates of executive board members were "to ensure the political independence of central bankers from elected politicians, whose mandates are shorter," said Thorsten Polleit from Barclays Capital.
"Political interests have led to this rule being suspended, which is hardly advantageous for the ECB ... If you break one rule it opens the door to others being bent," he told AFP.
Clemente De Lucia from BNP Paribas agreed.
"The best thing for Europe would be to have a central bank that is as independent as possible with members chosen on the basis of their qualifications, not their nationality," he told AFP.
German Chancellor Angela Merkel gave her crucial blessing for Draghi after German central bank governor Axel Weber quit the race in February.
Draghi already had the backing of the eurozone's 17 finance ministers and the European Parliament, but Bini Smaghi was holding out for the top job at Italy's central bank, citing the market-sensitive treaty guarantee of ECB independence from political interference.
Bini Smaghi will be one name on a three-man shortlist considered by the Italian government next week, sources said.
Nicknamed "Super Mario" at home, Draghi acquired international status during the global economic crisis by overseeing a process of reforms as head of the Financial Stability Board, a group charged by leading world economies to reform the world banking system.
He restored credibility to the Italian central bank on his appointment there in 2005 after it was tarnished by an insider trading scandal involving ex-governor Antonio Fazio.
He graduated in economics from Rome University and has a doctorate from the Massachusetts Institute of Technology (MIT) in the United States.