The Portuguese coach replaces Massimiliano Allegri, who was relieved of his duties after the club failed to achieve UEFA Champions League qualification.
Allegri's departure followed a disappointing campaign for the Rossoneri. Amorim himself exited Old Trafford in January after overseeing 63 matches in charge.
His spell in England was clouded by concerns regarding emotional inconsistency and a perceived lack of stability in his leadership style.
Further doubts stemmed from his reluctance to move away from his preferred 3-4-3 system, which ultimately weakened confidence in his methods at the Manchester club.
However, Amorim is eager for a fresh start at Milan, and delighted to be taking the reins at such a prestigious club.
"There are ambitions that stay with you throughout your career, and coaching AC Milan has always been one of mine," he stated.
"I know exactly what this club means: history, prestige and an extraordinary fanbase around the world. It is a challenge I embrace with pride and enthusiasm, fully aware of what these colours represent.
"I can't wait to get started and to experience every day the passion that drives AC Milan."
