The role had been vacant following Michael Dawson's move to Hull City this summer, but the French defender has been named as his replacement, with Emmanuel Adebayor and Hugo Lloris confirmed as vice captains.
Kaboul told the club's website: "I am delighted to have been given this responsibility. To follow in the footsteps of some of the legendary captains that have represented this football club is a fantastic honour.
"It is a great achievement for me on a personal level and I hope to help lead this team to great things in the future."
Manager Mauricio Pochettino added: "Younes has shown me all the values needed to be a captain. He has the character to lead this team as well as the respect of his teammates. Hugo and Ade will be vice captains and both of them, along with Younes, possess tremendous experience and have all shown a great attitude and leadership."
Kaboul has worn the armband in the five matches that he has started since Dawson's departure.