Cagliari have announced they have released Massimiliano Allegri from his contract "following a request from AC Milan", leaving him free to take over the reins of the Serie A giants.
Allegri was relieved of his duties at Cagliari in April but remained contracted to the Sardinian club until 2011.
The Milan vice-president, Adriano Galliani, confirmed last week they would name Allegri as their new coach as soon as they got the green light from Cagliari.
A statement on the Cagliari website read: "Despite the bitterness and disappointment left to us by the lack of interest shown by coach Massimiliano Allegri at the end of the championship, following a request by the AC Milan president, Massimo Cellino [the Cagliari chairman] decided to release him.
"Even having made him available to Milan, Cagliari have not requested any financial compensation, given the impossibility of quantifying the value of feelings.
"The only positive note is that the end of the relationship with Allegri allows us to draw a definitive line under it and we can dedicate ourselves to the future of Cagliari through the choice of a new coach."
The Rossoneri have been looking for a new coach since Leonardo parted company with the club after just one season in charge.
Allegri is regarded as one of the country's finest young managers, and the 42-year-old was voted the best coach of the 2008-09 season ahead of the former Inter manager, José Mourinho.