Young ends his eight-and-a-half-year stay at Old Trafford and joins Antonio Conte’s men who are second on the Italian Serie A table, two points behind Juventus.
The 34-year-old was signed by Sir Alex Ferguson in the summer of 2011 from Aston Villa and he went on to make 261 appearances for the Red Devils, scoring 19 goals.
Young won all domestic cups in England during his time at United and also added the 2016/2017 Europa League to his trophy collection at the club.
The former Watford winger is the third United player to swap Old Trafford for the San Siro in less than a year after Romelu Lukaku and Alexis Sanchez made similar moves in the summer.
Young posted on his social media: "To Man Utd, you gave me the chance to play with legends, to win trophies, to work under the greatest manager in history and to be your captain.
"Thank you for letting me be part of your story for eight-and-a-half years.
"To the United fans, every time I walked on the pitch wearing your shirt I gave you my all. Thank you for your support during the highs and the lows. I leave as one of you, see you again in an away end soon."
Young’s position as Manchester United captain has now been taken by summer signing Harry Maguire, who joined for a record fee of £80m from Leicester City.
