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Robertson, who was part of Team Cricket's set up in the most recent edition of the event, will switch sides for 2021.
"I think Ted (Henry) is making up for not giving me the All Blacks job," Robertson said of his switch.
"He's brought me back over now so we can rebuild that relationship, which I'm really thankful for by the way, Ted. I have gotten over that emotionally and I'm looking forward to it and on January 22nd I'll be right beside you mate, whatever you need."
Robertson missed out on the vacant All Blacks job when Steven Hansen departed following the Rugby World Cup, with assistant coach Ian Foster being promoted to the head coaching role.
Henry was a member of the selection panel tasked with appointing the next person to lead the national team, with Razor revealing in April that Henry cornered him with difficult questions during the interview process.
"I had bought a new suit for the presentation and in the end I just thought: 'I'm just going to be myself', and then the questions just came at me," Robertson said on the Will Greenwood podcast.
"And they were great – I wanted them to challenge me. Graham Henry was on the interview panel and was really deep. He put me in a corner with a couple of questions and he wouldn't let me out. It was quite a challenging moment and made me think. I left like I maybe hadn't articulated myself as well as I could have or should have."
Henry has previously expressed his admiration for Robertson's coaching ability, but admitted now wasn't the right time for the young coach to take the next step into the All Blacks' top job.
"I think he's got the passion to coach the All Blacks and that's what he really wants to do and I think it's in his psyche," Henry said after Foster was announced as the next All Blacks coach late last year.
"I think he will be the All Black coach, it's just a matter of time. He's 45, isn't he? He's just a baby as far as coaches are concerned, very talented, very enthusiastic ... he's just got to be a bit patient."
The two will lead Team Rugby in the classic code clash, which will return to Ōtautahi Christchurch's Hagley Oval under floodlights on Friday, January 22.
The third annual T20 Black Clash, pitting Team Rugby against Team Cricket, is set to the first major event to be played under the brand new floodlights at Hagley Oval.
Team Rugby, inspired by Jordie Barrett and some brilliant out-fielding by Richie McCaw and Kieran Read, caused a shock by upsetting Fleming's cast of international cricketers in the opening encounter in 2019, before the cricketers got in the win column in 2020.
"It was pretty obvious that the 2019 result was just one of those freak occurrences that happen in sport," Team Cricket captain Stephen Fleming said.
"There's no rational explanation as to how it happened – and there's certainly no way anyone can foresee it happening again.
"We've got a lot of respect for Sir Graham's team – as rugby players. But as cricketers… not so much."