The 33-year-old, who made 189 appearances for the Reds during a five-year spell at Old Trafford, will join up with former manager Jose Mourinho, who also coached him at Chelsea between 2013 and 2015.
He's signed an one-year contract with the Giallorossi, who were recently crowned the first-ever Europa Conference League winners, after beating Feyenoord 1-0 in the final.
Matic confirmed in April that he would bring his time at United to an end, upon the expiry of his contract, and he was included on our list of 11 released players submitted to the Premier League on Friday.