And the rising defensive star has now completed his switch to San Siro, where he will reunite with coach Sinisa Mihajlovic, under whom he worked while on loan at Sampdoria last season.
Confirming the news via a welcome note on their official website, Milan said: "Welcome Alessio, you've signed with us until June 2020 and we're very happy about it.
"You're a young man, you're 20, and because of that we believe you have all the time in the world to become an icon of our club, following the path of the great Rossoneri defenders. A big hug from AC Milan, and forza Alessio."
Romagnoli made a total of 31 appearances in 2014-15, scoring twice.
"Mihajlovic knows him well," he told Milan Channel.
"If he wanted him so much it’s because he knows he will be very useful. We will do everything to help him integrate as soon as possible.
"I know him from our time at Roma, he is a great signing."
Roma later confirmed that the Italy Under-21 international was sold for €25 million, before adding: "In the eventuality that Romagnoli is sold on, Milan have also agreed to pay Roma 30% of any amount higher than €25 million."