Terry, 35, signed a new one-year contract at Stamford Bridge in May to end speculation that he was going to leave the London club after more than 700 appearances. He remains a firm favourite with the club's fans.
“John Terry is captain of this team. He is a great player with a great personality and charisma. He knows the club. We take all decisions together with the club and I am very happy John signed,” Conte said.
Conte, who guided Juventus to three successive Serie A titles from 2012 to 2014 before becoming the Italian national team coach, has replaced interim manager Guus Hiddink.