The club is expected to make a statement later today but Neil Lennon said: "I have parted company with Celtic.
"I can't thank [chief executive] Peter Lawwell and the board enough for their backing and support during my time as manager.
"The club are in a very strong position and I wish the fans and the club all the very best for the future."
Lennon has led the Parkhead club to three successive Scottish titles since succeeding Tony Mowbray as boss back in 2010.
And he also guided the Glasgow giants into the knockout stages of the Champions League last season - after beating Spanish superstars Barcelona in the group stages.
He has been linked with moves to Barclays Premier League clubs in England as a result of that domestic and European success with the Hoops.
Last season he was tipped to take over from Davie Moyes as Everton manager and this season he has been touted as a possible successor to Chris Hughton at Norwich City.
Lennon is rumoured to believe that he has taken Celtic as far as he can.
And he has spoken in the past of his desire to manage in England - where he played at the start of his football career with Manchester City, Crewe Alexandra and Leicester City.
Nobody at Celtic was available to comment today, but the club were set to release a statement on their official website.
His future at the club has become increasingly uncertain in the past few days with rumours swirling that he was set to leave for a job down south.
Speculation has also been rife about who will succeed him in the Parkhead hotseat.
Among the names touted have been former Cedltic legend Henrik Larsson and former players Davie Moyes and Malky Mackay.
His ex-deputy at Celtic Park and former team mate, Johann Mjallby, has also beemn suggested as a possible successor.
The crowning glory of Lennon’s reign was the 2-1 victory over Barcelona that took the club into the group stages of the competition.
Lennon has been a controversial figure in Glasgow and has often clashed with authority.
He was assaulted in the street after a night out in Glasgow’s west end and two men were jailed for sending devices through the post.