Lennon 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.
However, Celtic are well behind their Glasgow rivals in their bid to win 10-straight titles and slumped to defeat at struggling Ross County on Sunday.
Assistant manager John Kennedy will take interim charge of the team.
“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, 49, said, in a statement on Celtic’s website.
“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.
“I have always given my best to the club and have been proud to deliver silverware to the Celtic supporters. The club will always be part of me. I will always be a Celtic supporter myself and I will always want the best for Celtic.”
Celtic said former captain Lennon had “served the club with distinction as both player and manager”.
“Neil has always been and will always be a true Celtic man and someone I will always hold in the highest regard,” added chief executive Peter Lawwell.
“Personally, it is a sad day for me to see Neil leave. Neil is a man of quality and decency, he is someone who will always be part of the fabric of Celtic and someone who will always be welcomed.”
Principal shareholder Dermot Desmond described Lennon as a “Celtic legend”.
“He has given so much to the club, and with his success over the last number of years – including winning a treble in his own right – he will be very difficult to replace,” Desmond added.