The 28-year-old academy graduate takes over the armband after long-serving skipper Scott Brown left for Aberdeen.
Manager Ange Postecoglou explained that Scotland midfielder McGregor, who has made 326 appearances for Celtic has shown all the qualities he requires from his captain.
“Callum is a player who leads by example, both on and off the park, and he is a key figure in our squad,” said Postecoglou.
“He has been at Celtic since he’s been a boy, had a loan spell away from the club to gain vital experience, and then returned to establish himself in the first-team. His qualities as a player are there for all to see.
“He knows what it takes to be a successful Celtic player, and he knows what it means to captain this club, and I’m delighted that he will be wearing the armband and leading the squad going forward.”