The defender concedes he was concerned about his renewal as he had spells out last season with injury.
He told AS: "When I was injured I had not completed the number of games for the renewal. Logically, you don't know if you're going to return early or not, but from the first day at the club they gave me the confidence not to worry about that situation, that they wanted me next season.
"And no doubt. From there the recovery went very well, afterwards was when I felt better at Atleti. I face this season with great enthusiasm. When I arrived I had the ambition and hope of winning titles with Atleti. Last year we didn't make it and this year I'm even more looking forward to it."
On Alvaro Morata's departure for AC Milan, Azpilicueta added: "Álvaro has been a teammate of mine at Chelsea, the National Team, Atleti... Always willing to help everyone, the kids, always with a smile. We are sad because he is leaving a very important player in the team. Wish him the best."