It was widely reported for some time that the Northern Irishman would leave his post with the Glasgow club, with speculation suggesting that Lennon had taken them as far as it could go with him at the helm.
The former Celtic midfielder, who made 214 league appearances for the Hoops, joined the club following Tony Mowbray's departure in 2010 and guided the Glasgow outfit to three Scottish Premier League titles and two Scottish cups.
"I have supported Celtic all my life and the club will always be part of me," Lennon told Celtic's official website.
"It was an absolute honour to play for this great club, to captain the team and of course to become Celtic manager, a position which I cherished dearly.
"However, I feel the time is now right to move on to a new challenge.
"Of course, I am very pleased that I will be leaving Celtic as Scottish champions and with the club in such good health. I wish the club nothing but good fortune going forward.
"Serving the club was always a privilege. I have always given my best and aimed to do all I can to ensure success for Celtic, as a supporter it was all I wanted.
"I will now assist the club in appointing my successor. As ever, we will need our fans' support and I am sure they will give the club and the new manager the same great backing which they gave to myself."
Former Sweden striker Larsson - who scored 242 goals in 315 games for the Glasgow club between 1997 and 2004 - has hinted that he is open to replacing Lennon.
Larsson is manager of Swedish side Falkenbergs. He had also spent three years as a coach with Landskrona.
"When I stopped playing football and went into management, I knew the Celtic job was one that I would be linked with," said Larsson to STV.
"I have and always will have a strong affection with the club. It’s not a question whether I’d be up for it. At the moment I’m only focusing on the job at Falkenberg.
"I can see myself back at Celtic, whether it’s now or in the future time will tell. That’s all I’m going to say, it’s up to you to work out if there’s been contact.
"Neil has done a great job and his achievements shouldn't be overlooked just because Rangers haven't been in the league. Reaching the last 16 of the Champions League showed that he's a great up and coming manager.
Martin Reilly - who represents the Northern Irishman Lennon - said that after four years and three title wins, the former club captain had decided he wanted to take on a fresh challenge.
He told Press Association Sport: "Four years is a good spell to be manager of a club like Celtic, but now Neil wants to look ahead to the next chapter of his career."
Former Manchester United manager David Moyes, who played for Celtic in the 1980s, has also been linked with the job.
William Hill tweet: Following Celtic's announcement of Lennon's exit, Henrik Larsson is 4/11 favourite to replace him. pic.twitter.com/wLecJHPBYC
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