The 35-year-old defender signed a one-year contract extension - his third such deal - in May, having in January declared his expectation that he would leave this summer.
Terry, who has made more than 700 appearances for the Blues, has been reassured his considerable influence is valued.
"Yes, John Terry is the captain of Chelsea when he plays, when he doesn't play. You are always the captain," Conte said as he was unveiled as Chelsea head coach at Stamford Bridge on Thursday.
Mercurial Superfly VI heritage "He's captain of this team, he's a great player, with a great personality, with great charisma.
"I like to speak to him because he knows the club, the right spirit to play in this club and for me he's an important player.
superfly mercurial iv pink "When a player deserves to play, with me, (they) play."
Former Italy boss Conte, speaking English well, expressed his pride and excitement at what awaits with Chelsea.
He also acknowledged the challenge ahead at a club which won the 2014-15 Premier League title, but finished a lowly 10th last term.
"The pressure for me is not important," Conte added.
"I was born with pressure. It's normal.
"When you are a player, a footballer, or a manager of a great club like Chelsea you must play to win the title or to fight at the end to compete with the other teams, to win the title, to reach your targets.
"I know this league is very, very difficult, because there are six, seven teams that can win the title.
magista obra fg black "We know that this year it won't be easy for us because if we think the last season 10th position, last season was a bad season. We know. Me, the players, the club.
magistaX proximo ic orange "But I think we must think to the present, to work very hard every day, every week, every month, to build something important for the club.
"The fans need to find a team ready to fight until the end to compete with the other teams. There is only one team to win the title, but we must stay there till the end of the season.
what is the mercurial "Chelsea belongs to Champions League and we must stay there."
