Largely unknown outside Italy, Allegri cultivated an attractive brand of attacking football when leading unfashionable Sassuolo to promotion to Serie B in 2008.
He was then plucked from obscurity by top-flight side Cagliari where he continued his good work for two seasons.
"Today is the first day. Now I will have time to think and a month available to prepare for the new season," Allegri told Milan's television channel after signing a two-year deal.
"Coaching Milan represents a very important point of arrival in my career. I'm part of one of the strongest clubs in the world."
"GOLDEN BENCH"
Allegri proved his ability by winning Italy's "Golden Bench" award in February after his peers voted him Serie A boss of the year for his attacking play and good use of modest players and funds.
Allegri's move to Milan took several weeks to be finalised because he was still contracted to Cagliari despite being sacked. Club president Massimo Cellino was reluctant to let him go given his anger at the coach's last few months in charge.
"The negotiations extended for a month but luckily everything ended well," Allegri added.
"I replace Leonardo, a coach who has done a good job. Under his leadership Milan fought until the end for the scudetto and the team played very well. Therefore I receive a very important legacy."
