The Blues announced on Wednesday that Wright will be Carlton CEO Brian Cook's deputy before taking the reins via a handover plan, delivering a stinging blow to their fierce AFL rivals.
Wright, the mastermind behind Collingwood's 2023 premiership, quit the Magpies following a leave of absence this year.
A 1990 Collingwood premiership player, Wright, 56, spent an extensive period at Hawthorn, where he was instrumental in building the list that won four premierships.
He moved to Collingwood in 2021, and two years later delivered the 2023 premiership, before taking an overseas sabbatical, following 35 straight years involved in the AFL.
He ultimately didn't return this season, when Collingwood failed to make the finals, with his departure announced in August.
Asked if there were "creative tensions" with Kelly, and if that contributed to his exit, Wright said: "No.
"There was always a chance (I would move on).
"I mean, I actually resigned, where they wouldn't accept my resignation.
"But, yeah, there was always a chance that I'd do something else or look to do something else, and that became clearer for me towards the back end of July."
Reflecting on his time at Collingwood, Wright said: "I had some great times there.
"There's some fantastic people there and I wish everyone at Collingwood well, except when they're playing Carlton.
"But I hope they do well and I've got a lot of friends there, so there was no issue with that."
From left, Carlton CEO Brian Cook, president Luke Sayers and new deputy CEO Graham Wright. (Joel Carrett/AAP PHOTOS)
Wright was in heavy demand, with the AFL interested in securing his services, while Adelaide had also tried to lure him to oversee their football program.
But the opportunity to become Carlton CEO, after previously working in football roles, piqued Wright's interest.
"I acted in the role (CEO) for three or four months at Collingwood, and that probably whet my appetite for it," he said.
"I felt and believed that I had more to give than just football.
"So when that opportunity was there, and particularly to work with Brian, I was really excited."
Securing Wright is a huge coup for Carlton, who are attempting to bounce back from their meek elimination-final exit.
"In my opinion, in the board's opinion, we've appointed the best football person in the country to lead our football club," president Luke Sayers said.
"Graham's proven ability to take a football club from good to great is, in my opinion, in the board's opinion, unmatched, and will be an invaluable asset as this club looks to evolve to the level required to contend for premierships into the future."
Wright will start on Monday but won't have any direct reports as he learns from Cook.
"We're looking towards his advice on the trading period, which might be a little bit different than what we have at the moment," Cook said.
Wright wouldn't be drawn on whether he would get involved in dealings for Port Adelaide's Dan Houston.
Cook, contracted for 2025, said he was "fully supportive" and "extremely comfortable" with the handover plan.
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