The Frenchman has joined the Rossoneri on a free transfer from Roma and is looking forward to the challenge.
"I want to give my best on the pitch for the club, the Coach, my colleagues and the fans," he told Mediaset's Studio Sport.
"I will have the honour of wearing this shirt for a minimum of four years and this club is the maximum for any footballer.
"I'm not presumptuous enough to think that I will be an heir to Franco Baresi or Alessandro Costacurta.
"Winning is enough for me. I want to lift as many trophies as possible."
Mexes has been a familiar face in Serie A for some years now after making his reputation with the Giallorossi.
"I had seven wonderful years at Roma and they will always be in my heart," he added. "I got to know Italy there and I hope that my former teammates do well in the future.
"I leave behind many friends and I'm proud of my time there. I say goodbye and thank you to everyone, my teammates, the club and my Coaches."