The Glasgow club relieved Thompson of his duties via telephone on June 3, after he alledgedly refused to attend a meeting with manager Neil Lennon.
The 38-year-old immediately signalled his intention to fight the Glasgow outfit for compensation, claiming that he had been wrongfully dismissed.
However, the legal dispute has now been resolved "amicably", just three weeks after Thompson's initial dismissal.
A statement on the club's official website read: "Celtic PLC and Alan Thompson are pleased to advise that they have reached an agreement to amicably settle their legal dispute.
"Celtic PLC extend their thanks to Alan for his services to the club as a top-level player and a first-class coach.
"Alan would like to express his deep gratitude for the overwhelming and heartfelt backing he has received from Celtic fans everywhere, and for the support of his legal team at Bridge Litigation UK Solicitors.
"Alan intends to continue his coaching career, building on the invaluable experience gained during his time with Celtic.
"Alan wishes Celtic Football Club and the fans every success for the future.
"Celtic would like to thank Alan for the contribution he has made to the club over a number of years as both a player and a coach, and we sincerely wish him well for the future."