The former England international joined the club he used to play for as a coach in June 2010, and his lawyer revealed that he was notified of the decision by manager Neil Lennon
The former midfielder, who used to play for the Glasgow side, was appointed to the backroom staff at the club in June 2010 alongside assistant manager Johan Mjallby by boss Neil Lennon following Tony Mowbray's dismissal.
"I can confirm that I have been instructed to act on behalf of Alan Thompson following his dismissal by Celtic FC," his lawyer, Margaret Gribbon stated.
"Alan was informed of the decision to terminate his employment with immediate effect in a telephone conversation with the club manager Neil Lennon."
Thompson played for the club for seven years between 2000 and 2007, winning four league titles and three Scottish Cups, and is also a former team-mate of Lennon.
The 38-year-old has been linked with a move to Aston Villa, which would see him reunited with former Celtic midfielder and new Villa boss Paul Lambert.