The Swede took to Instagram to say goodbye to the club and the fans, vowing to return for the 10 in a row party.
Lustig's contract with the Parkhead side expired at the end of May and he is expected to sign a deal with Belgian side KAA Gent.
It ends a seven-and-a-half year Celtic career having joined from Rosenborg in 2012.
He made more than 220 appearances for the club, winning eight league titles, four Scottish Cups and a quartet of League Cups.
Lustig posted: "I had no idea how much this club and everything that comes with it would mean to me when I signed 7.5 years ago. It's time for me and my family to move on, start a new chapter in life.
"To make a post on Instagram isn't enough to express my feelings and thoughts about the situation. I wish I would've had the chance to say a proper good bye.
"I just want to say thank you to everyone I've had the honour to meet and work with at Celtic, all the players and staff. The memories will stay with me forever.
"Thank you to all of you that made Glasgow feel like home for me and my family for so many years. I will never forget your support.
"Hopefully I'll see you all soon. I'll definitely be back for the 10 in a row party!"