The experienced sports executive takes charge at a pivotal moment for the Rossoneri under RedBird Capital Partners.
Calvelli arrives with extensive international experience across the global sports industry and will continue to serve as CEO International at RedBird Development Group and Operating Partner at RedBird Capital Partners alongside his new role at San Siro.
RedBird founder and managing partner Gerry Cardinale believes the Italian is ideally placed to drive the club forward after spending the past year working closely with Milan's leadership.
"Since joining RedBird last year, Massimo has distinguished himself as a leader and driver of organizational design that brings people together and establishes a culture of collaboration and professionalism," Cardinale said.
"Our model at RedBird often requires our senior leadership to go 'in house' in our most important investments to ensure best in class execution. The mandate is clear - we will play to win, instead of playing not to lose - in everything that AC Milan touches, but most importantly on the field."
Calvelli said he is fully aware of the responsibility that comes with leading one of European football's most decorated clubs.
"The opportunity to lead AC Milan as it navigates this critical moment in its football trajectory, as well as within the overall state of Italian football, is something I take very seriously and with a profound sense of urgency," he said.
"The mandate from Gerry is to bring a culture of winning and results both on and off the field back to AC Milan - a culture worthy of the heritage that the Club represents within the European football community and our over 500 million fans worldwide."
He also revealed he is eager to work alongside new head coach Rúben Amorim.
"I've had a full year working collaboratively with the senior leadership of the Club across all functions and have a hands-on sense of what needs to be fixed and innovated. I'm personally excited to work closely with our new Head Coach Rúben Amorim and his team."