Igesund said on Friday he had spoken to Khune, who is known to lose his cool with match officials, and told him to dial down his temper.
"To be a great captain he just has to calm down in certain situations," Igesund said at a Bafana training session in Germiston.
"Sometimes he loses his temper, but I've spoken to him about that and a lot of things.
"There's hundreds and hundreds of captains, there's only a few great captains."
The Bafana coach ended speculation on the Bafana captaincy by naming Khune as permanent skipper ahead of a friendly international against Lesotho on Sunday, and World Cup qualifiers against Central African Republic and Ethiopia.
"Let me take this opportunity to say that Itu is the captain of the national team from now on," Igesund said.
The coach was unsure, however, whether Khune would play in Maseru this weekend, confirming either Senzo Meyiwa or Wayne Sandilands could be given the gloves.
"Well I'm not sure he's going to play at this stage," he said.
"If I decide to rest him or use him, there will be a stand-in for the day of the match, but it won't be changing on a regular basis."
Khune, the captain of Premiership champions Kaizer Chiefs, said he would have no problem stepping up.
"It humbles me as a person and it will improve my leadership skills," Khune said.
"It's a heavy responsibility. In the past games the players have responded well from what the coach has told me to tell them. I'm happy, but again I'm humbled."