"The European Council has just agreed on the appointment of Mario Draghi as new president of the ECB," Van Rompuy, who chairs EU leaders' talks, said in a message posted on Twitter.
Draghi's much expected appointment did not come without controversy, as countries, in particular France, haggled over their country's representation on the ECB Board.
Sources indicate that French leaders were annoyed that they would have no representative on the six-man executive board once Jean-Claude Trichet's tenure as president ran out. Draghi's appointment would leave Italy with two members.
As a result, Italy's European Central Bank executive board member, Lorenzo Bini Smaghi, has given verbal assurances that he will step down from the central bank board before Italian Mario Draghi takes over as ECB president in November, EU sources said on Friday.
The sources said Bini Smaghi, who was not due to leave the board until May 2013, had spoken by phone to Herman Van Rompuy, the president of the European Council, and French President Nicolas Sarkozy on Friday to say that he would step down sooner.
"We expect an announcement shortly," one senior EU source said. Another said: "This morning, in the Council, Van Rompuy and the Italians will explain that Bini Smaghi will leave in due time."
The French expect to appoint a French national to the upcoming vacancy to ensure they have representation on the board.
Sources also say that Bini Smaghi was using his resignation as a bargaining chip in return for being given Draghi's current job as governor at the Banca d'Italia.
EurActiv with Reuters