A club statement said: "Celtic Football Club today announced that Neil Lennon has resigned from his position as football manager with immediate effect.
"Neil has served the club with distinction as both player and manager, delivering numerous successes, most recently completing the domestic treble in December."
The 49-year-old said he had failed to turn around a difficult campaign and felt it was in the best interests of all parties he stepped down.
Celtic trail Rangers by 18 points in the Scottish Premiership.
"We have experienced a difficult season due to so many factors and, of course, it is very frustrating and disappointing that we have not been able to hit the same heights as we did previously," Lennon said in a statement.
"I have worked as hard as ever to try and turn things around, but unfortunately we have not managed to get the kind of run going that we have needed."
Lennon was in his second spell at the club and guided them to two league titles, two Scottish Cups and a League Cup after replacing fellow Northern Irishman Brendan Rodgers in 2019.
Assistant manager John Kennedy will take interim charge of the first team.
