The veteran has signed with Roma as a free agent.
The Serb said: "With Mourinho we know each other well and I am happy to find him here. I am here for him, but I am happy to be part of this great club, he is attractive to the players and he has been for me. I am looking to beat (Frank) Lampard as the player with the most appearances with Mourinho.
"I think the team has great quality players with young players who can be important in the future. I can't wait to get started.
"After eight and a half years I wanted a new experience. Rome is an important challenge, Serie A too. I could have stayed in the Premier League, but I decided to try in Italy. There are many clubs, it is a great league.
"I am convinced that I have made the right choice. Revolution in Manchester? It hasn't won titles for several years, it will certainly improve and I wish them the best. It is difficult to say then what will happen, but I have been there. I was very happy."
Matic added: "The negotiation was quick because the ambitions of the club and the coach are the same as mine. The victory of the Conference did not affect my choice, because it was an easy choice. When I make a decision, nothing makes me change my mind."