The 32-year-old defender was limited to 27 appearances in all competitions for the Blues last term under Roberto Di Matteo and Rafael Benítez.
But Mourinho, who was officially unveiled as Chelsea boss on Monday afternoon, says he is “more than happy” for Terry to continue to lead the west Londoners.
“Last time John was the captain by a club decision, because he was born in the club and because of his personality on the pitch. I did a simple consultation with the players trying to feel opinions and everybody agreed.
“At this moment, when you say “my captain”, it’s not the real word. It’s more Chelsea captain, because Chelsea captain is my captain, the board’s captain, the fans’ captain.
“John is the club captain; I’m more than happy he’s the captain, the fans are more than happy he’s the captain, so I think he has to be.
“Has he the armband? Only if he plays. If he isn’t in the starting 11 he doesn’t have the armband, but he’s the captain.
“I didn’t think for one second before on this but he has to be and he deserves to be, I’m happy for him to be.”