Loftus-Cheek has signed a four-year contract with the Rossoneri, who have paid Chelsea £15m for his services.
Loftus-Cheek joined Chelsea's academy in 2004 and spent 19 years on the club's books, though he spent season-long loans at Crystal Palace and Fulham along the way.
In total, Loftus-Cheek made 155 appearances for Chelsea, scoring 13 goals and winning the Premier League, Europa League and UEFA Super Cup.
In a farewell message to Chelsea fans on Instagram, Loftus-Cheek wrote: “I don’t even know where to begin with this. I’ve been at Chelsea since the age of 8 and to come through the ranks and play senior football at this club… there’s just no better feeling. I’ve truly gone from being a boy to a man at this club over the last 19 years and it’s hard to say goodbye to so many people that have helped guide and shape me as the person and player I am today.
“It’s always been my dream to play for Chelsea so being able to win the FA Youth Cup and UEFA Youth Cup during my days in the academy, to then making my first team debut and winning the Premier League Europa League during my senior career, is something that I will cherish for the rest of my life.
“I would like to thank everyone associated with Chelsea football club who have helped me during my career. To the coaches that i’ve worked with, the backroom staff and my teammates to the people i’ve seen day to day at the training ground over the last 19 years, thank you all.
“To the fans, you’ve supported me and had my back from day one, no words will ever be enough to tell you how much that has meant to my family and I. I wish nothing but the best to everyone here and hope to see the club get back on the right path and winning silverware as soon as possible.
“It’s time for me to begin a new adventure in football, to live in a new country and experience a new culture, but I really do hope our paths will cross again in the future.
“Thank you for everything.