The 28-year-old had been heavily linked with a possible move to Orlando Pirates, and the player repeatedly denied any knowledge of the media reports.
Hunt was visibly happy when breaking the news to the media gathered in Parktown, where he was honoured with the Coach of the Month award for February.
Hlatshwayo's contract was only going to expire in June 2019, but the Students moved swiftly to fend off interest from the Buccaneers by tying their skipper down for the next three seasons.
“He [Hlatshwayo] has signed the extension now. So, that was put to bed,” Hunt told reporters.
“He's signed another three years. I know and I read about it [Pirates interest] and obviously it didn't make the boy's life easier because he was getting phone calls or whatever. He is okay and he is settled now,” he said.
Furthermore, Hunt revealed that Buhle Mkhwanazi has also been handed a contract extension.
However, he didn't reveal the length of the defender's new deal with the Clever Boys.
“Buhle as well he is fine. He got an extension, those are fine," continued Hunt.
“You always got to try and work six to eight months in advance. I think if you don’t and you wake up you get lost. We always try to work in advance even though you are worried about the situation, but you need to work in advance, that's the nature of the game,” he added.
The two defenders were believed to be on their way out at the club, especially after some wholesale changes Hunt made to his squad at the beginning of the season.
Edwin Gyimah's arrival as well as that of Dennis Weidlich sparked rumours that Wits could be preparing for life without Hlatshwayo and Mkhwanazi.
But with the new deals signed and sealed, whoever wants the two players will have to dig deep into their pockets to land their signatures.