The 37-year-old goalkeeper joined the Hoops on a free transfer in 2014 and won six league titles in Scotland.
Gordon rejected a new contract offer due to his desire to play regular football again.
He has played second fiddle to Fraser Forster this season as the 32-year-old returned on a season-long loan from Southampton last summer.
Gordon, who has been linked with a summer move to Hearts, said: "Six league titles. Five League Cups. Three Scottish cups.
"The last six years have been the most successful period of my professional career, and I would like to thank everyone who has played their part in making this possible.
"The club, for initially taking a chance on someone who hadn't played in nearly three years [due to knee injuries].
"And to Woodsy [Celtic goalkeeping coach Stevie Woods] for encouraging me to make the move in the first place, and for training me ridiculously hard ever since.
"I've had the pleasure of playing alongside some brilliant teammates - who without, my time at the club would have been very different.
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"The fans, for their support. Home, away… all over the world. Thank you.
"My family, who have been there through it all. The ups and downs, the miles, the sacrifices, the celebrations. I hope I've made them proud.
"At 37, and with a few years in me yet, I just want to play the game I love, and have played for 20+ professional seasons.
"Football can make for difficult decisions, but I'm looking forward to the next chapter and challenge.
"Thank you, again. CG."
View this post on Instagram
6 League Titles. 5 League Cups. 3 Scottish Cups. The last six years have been the most successful period of my professional career, and I would like to thank everyone who has played their part in making this possible. The club, for initially taking a chance on someone who hadn't played in nearly three years. And to Woodsy for encouraging me to make the move in the first place, and for training me ridiculously hard ever since. I've had the pleasure of playing alongside some brilliant team-mates - who without, my time at the club would have been very different. The fans, for their support. Home, away… all over the world. Thank you. My family, who have been there through it all. The ups and downs, the miles, the sacrifices, the celebrations. I hope I've made them proud. At 37, and with a few years in me yet, I just want to play the game I love, and have played for 20+ professional seasons. Football can make for difficult decisions, but I'm looking forward to the next chapter and challenge. Thank you, again. CG.
A post shared by Craig Gordon (@craig_gordon1) on Jun 28, 2020 at 10:52am PDT
Craig Gordon has confirmed his Celtic exit in a heartfelt Instagram post.