Milan icon Maldini replaces Leonardo in the post, with the Brazilian reported to be returning to a similar post at former club Paris Saint-Germain.
Boban, who played for the club between 1991 and 2001, has left FIFA, where he was the body's deputy secretary general, to return to Milan.
Maldini previously worked as Milan's sporting strategy and development director but Ivan Gazidis, the club's chief executive, feels he is the right man to succeed Leonardo.
"Paolo embodies that quality and those values that are the building blocks of our club," he said. "I am happy to have him at the helm of our sporting area.
"With him, we will be able to build a modern club, formed by professionals of the highest quality. It will be a journey we will pursue together to achieve a challenging and compelling project, one which will require great energy and dedication.
"I am confident Paolo will be able to project his experience, his vision and his leadership. Paolo is an integral part of AC Milan and knows the way to success. He will be an important point of reference for everyone."
Boban and Maldini will work closely together, with the former team-mates reuniting on the Rossoneri's backroom staff.
"I am very happy to return to my beloved Milan and I will give my contribution to bring it back where it deserves to be," Boban said via a Milan statement.
"Milan must be a leading and winning club, because this is the only nature of its history and it's the nature of our fans and their passion. I will give all of myself for this cause and for the Rossoneri colours.
"When Paolo called me to check on my availability, I jumped into my car and went to his home in Milan in the middle of the night.
"After talking with Ivan and the club, everything was clear. And here I am, in my city, in my club I love and in a land that has given me so much. I hope I can repay the trust placed in me."
Milan is still seeking a successor to Gennaro Gattuso as head coach, but is reportedly close to appointing Marco Giampaolo from Sampdoria.