The 35-year-old signed a one-year contract extension – his third such deal – in May, despite having declared in January that he expected to leave the club this summer.
Terry, who has made more than 700 appearances for the Blues, endured a frustrating bit-part role at times during Jose Mourinho’s second spell at the club, but has been reassured about his position at Stamford Bridge.
And, speaking at a press conference for the first time as Chelsea manager, Conte insisted he values the former England international’s influence and experience.
“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 the Blues’ new head coach on Thursday.
“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.
“When a player deserves to play, with me, they play.”
Conte admitted during the conference that his English wasn’t quite up to scratch and is still learning the language, but, in truth, he spoke well in his first official appearance at Stamford Bridge.
He also acknowledged the challenge ahead at a club which won the 2014-15 Premier League title, but finished a lowly 10th last term, but insisted the pressure does not faze him.
“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.
“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.
“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.
“Chelsea belongs to Champions League and we must stay there.”