Former Wigan Athletic man leaves Newcastle
Caldwell had been working for the Magpies - with whom he started his playing career - as interim Under-23s lead coach.
He stepped in on a short-term basis last month following the departure of Chris Hogg, with the club poised to announce a full-time successor.
"Enjoyed immensely being back on the grass coaching at the club that gave me my start in football," he tweeted. "Thank you to all the players and staff for making me feel so welcome.
"Wish you and all the Newcastle fans the best of luck for the rest of the season. A fantastic football club.
"Looking forward now to my next challenge in the game which I will announce in the next few weeks.
Newcastle tweeted: "The club would like to thank Gary for his contribution and wishes him well for the future."
Caldwell has already been linked with Oldham Athletic, who are struggling in League Two after a poor start to the campaign.
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