Wednesday's 4-0 humiliation by St. Mirren proved to be the final straw for Mowbray who leaves the Glasgow club a distant second in the SPL, 10 points behind leaders and bitter rivals Rangers.
Former captain Neil Lennon has been placed in temporary charge of the first team, the club said.
"On behalf of the board and everyone at Celtic Football Club, I would like to offer Tony Mowbray my thanks and sincere best wishes for the future," chairman John Reid said in a club statement.
"Tony is held in great affection by Celtic fans and it is obviously with great disappointment that we make today's statement."
Mowbray, a defender at Celtic in the 1990s, took over last June from Gordon Strachan after gaining a reputation for attractive football at English club West Bromwich Albion.
However, a Champions League exit to Arsenal was compounded by failure in the Europa League in which they won only one of their six matches.
Mowbray's real problems have been in the SPL though where Celtic have failed to keep pace with Rangers and Wednesday's defeat at St. Mirren ended any slender hopes they had of making a late challenge for the title.
"This is a very sad day for everyone at Celtic," chief executive Peter Lawwell said. "Tony is a very fine man and someone who I know is passionate about the club he served so well as a player.
"Clearly, we have had a difficult season and results have not been as we would have hoped."
Mowbray, in a statement released by the League Managers' Association, said:
“Naturally I am very disappointed to be leaving Glasgow Celtic. I am very proud to have not only managed but also played for a club with such great tradition and that has tremendous roots in football history.
"I would like to offer my sincere thanks to all of the players and also to my staff who supported me so well. Finally, I would like to wish the club every success in the future.”
Commenting on Mowbray's departure, LMA Chief Executive, Richard Bevan said:
"It is disappointing that Celtic have parted company with Tony despite being in charge for less than a year, especially when taking into account that the club still have a great chance of silverware this season having reached the semi-finals of the Active Nation Scottish Cup.
"I am positive that a manager of Tony's calibre, with his success at WBA and Hibernian, and with an overall managerial win ratio of a soaring 45% in 297 matches in charge, will be back in management in the not too distant future."
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