The 26-year old Brazil international has been set for an Eastlands exit for some time and City were finally able to rid themselves of him for £22million.
City are said to be relieved to get his massive wage bill off their books and will receive an initial £18million with £4million in bonuses according to Mirror Football.
Robinho said he was delighted to have joined AC and plans to be successful at the San Siro.
"I hope to meet my new team-mates and become a champion with them,” he said after his medical this afternoon.
"I'm very happy. Milan are an excellent club."