Wright has been in the United States and Europe with his wife Tracey since March.
After being a mastermind of Collingwood's premiership last year, the 56-year-old wanted a break following 35-straight years involved in the AFL, first as a player, then in various off-field roles.
The Magpies were adamant Wright would return to his role refreshed, but he instead exits the club having been on leave during the entire home-and-away season.
"We have been in constant discussions with Graham during his sabbatical and both of us have agreed that Graham be free to pursue new opportunities to further develop his already distinguished career," Magpies president Jeff Browne said.
"All of us at Collingwood wish Graham, his wife Tracey and children James and Ethan all the best and every success for the next chapter."
Thank you, Wrighty �— Collingwood FC (@CollingwoodFC) Our Executive General Manager of Football Graham Wright will not be returning to Collingwood following his sabbatical.Details: https://t.co/ZQDQLfmkHb pic.twitter.com/5NoVB4NVraAugust 19, 2024
Wright, a 1990 premiership player with the Magpies, spent an extended period at Hawthorn under Alastair Clarkson before moving across to Collingwood in 2021.
When the Magpies announced Wright's sabbatical last December, Collingwood chief executive Craig Kelly insisted the club wanted to "normalise this type of leave for our key people".
During Wright's absence, the crucial role was mostly filled by assistant coach Brendon Bolton.
Collingwood are set to become the third reigning premier in four seasons to miss finals, entering the last round as only a mathematical chance to finish inside the top eight.
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