The Northern Irishman took charge for a second spell in February 2019 when Brendan Rodgers left and led the club to two titles, two Scottish Cups and a League Cup.
Celtic were chasing a historic 10th consecutive top-flight title this season but their campaign was thrown into disarray on and off the pitch.
The reigning champions are 18 points behind Rangers and defeat to Ross County on Sunday left Steven Gerrard's men just seven points away from the title.
Celtic also crashed out of Europe in the Champions League qualifiers and Europa League group stages, leading to fan protests outside the club's stadium and online calls from supporters for Lennon to go.
"Celtic Football Club today announced that Neil Lennon has resigned from his position as football manager with immediate effect," said a club statement.