Mourinho, who has signed a four-year contract on his return to Stamford Bridge, is keen to re-establish Terry as a key figure in the squad, after the centre-half, 32, was marginalised at times last season under interim manager Rafael Benitez.
However, the Portuguese coach – who guided Chelsea to successive English Premier League titles in 2005 and 2006 – maintains selection must always come down to individual form.
"Last time [I was manager], John was the captain by a club decision because he was born in this club, also, his personality on the pitch," said Mourinho. "I did a simple consultation with the players, and everyone agreed on that.
"At this moment, when you say 'my captain', it's not the real world. He is more Chelsea captain. 'My captain' is the board's captain, the fans' captain. I don't think the manager's captain is the correct word.
"John is the club captain. I am more than happy with that, so are the fans, so I think he has to be the club captain.
"With the armband? Only if he plays. If he isn't in the starting XI, he won't have the armband.
"I have not thought about that [who else would take over], but it has to be like that."
Mourinho is also in no doubt Manchester United made a "good decision" in appointing David Moyes as successor to Sir Alex Ferguson.
Mourinho, 50, was touted as a possible replacement for Ferguson at Old Trafford, with the 71 year old finally stepping aside at the end of last season.
The Portuguese coach, who has signed a four-year contract with Chelsea following his departure from Real Madrid, maintains Moyes deserves his shot at one of the highest-profile jobs in world football.
Speaking at this afternoon's official media unveiling at Stamford Bridge, Mourinho was pressed for his thoughts on the appointments of title rivals United and Manchester City, who are expected to unveil Manuel Pellegrini later this week.
"They have made good decisions," he said. "David proved himself at Everton. Okay, no trophies, but it's not easy to get a trophy when you manage Everton and he was not far from doing that.
"He has good experience, good work. I am more than happy, and I feel very happy for him.
"Man United will give him the time to adapt to a new dimension.
"He has never played a Champions League match so people can't expect him to be a fish in water in that first match.
"Give him time, stability. United is perfect for that, so that's a very good choice."
Despite being overlooked for the United hotseat, the former Porto and Inter Milan manager insists he would not want to be anywhere else.
"I am where I want to be. You tell me now every job in the football world at this table, I would choose my job. So I have the job I want to have," he said.
Mourinho also insisted he had no issues with Chelsea owner Roman Abramovich's reported interest in former Barcelona manager Pep Guardiola, who will take charge at European champions Bayern Munich next season.
The Portuguese coach said: "I don't know and I don't care, really.
"Roman never asked me if I had contact with other clubs, so I never asked him [about other managers]."
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