Cesare Prandelli has been named as the new Italy coach and will take on the role after the World Cup.
The Fiorentina coach will succeed Marcello Lippi, who will step down after the finals in South Africa.
The meeting came after Abete was given permission by the Serie A club earlier this month to talk to Prandelli, who has been in charge at Fiorentina since 2005.
He has signed a four-year contract, although Italian press reports claim some details are yet to be decide.
Announcing Prandelli as the new national boss, a statement released by the Italian federation (FIGC) said: “Cesare Prandelli will take over the bench from coach Marcello Lippi after the World Cup in South Africa.
“President Abete has confirmed this morning, in a meeting that was held in Rome, the contract with the next coach of the national team, after the decision of Lippi to leave his post.
“The FIGC and Cesare Prandelli have agreed a contract for four years. The details of the deal will be defined in the coming days.
“The official presentation of the new coach will be at the end of World Cup.”
Earlier Lippi had stated his belief that Prandelli was the best choice to replace him.
“I told the president Abete at Christmas that I intended to finish these two years and then leave,’ he said.
“Prandelli is the right person in the right place, but we will talk about this more in depth in the future.
“We will also talk further down the line, if you like, of the reasons which have pushed me to leave the national team for the second time.”