Khune replaced Tau on Tuesday with the latter suffering a reported fall-out with Amakhosi coach Vladimir Vermezovic.
"It is a great honour for me to captain the team thus leading a special group of players," Khune told Chiefs' website.
"I would like to thank the club for showing confidence in me by handing me such a huge responsibility.
"The coach called the whole team including the technical and football manager, Bobby Motaung to make the announcement on Tuesday. I cannot put the feeling into words of how it felt. I am supremely honoured."
The 24-year-old added that he will rely on Tau for assistance.
"Jimmy has been a great captain for the club. I continue to have respect for him for what the team has achieved during his tenure.
"I will be relying not only on him but all the players as we take the team to another level."