The Northern Irishman stood down from his post at Parkhead following four years with the Scottish champions.
The 42-year-old has revealed that he will help the club search for a new manager.
Celtic chairman Ian Bankier told the club's official website: "Neil has given a huge part of his life to serving the club and we will always be grateful for all he has given us.
"Ultimately, Neil brought Celtic back to the top of Scottish football, re-introducing the passion and drive which we needed to succeed and of course keeping us there for the last three years.
"Neil has shown the club a huge level of commitment and effort over his four years as manager. We thank him sincerely for all he has done and of course we wish Neil and his family the very best for the future."
Chief executive Peter Lawwell added: "I would like to thank Neil for everything he has done for Celtic. When we appointed Neil as manager we did so knowing exactly what the club meant to him and knowing that he would give all he had to the job.
"He has delivered great success to our supporters domestically and has brought us back to the table in European football. He will always be part of the club and we wish Neil and his family nothing but success in the future.
"We now embark on a new and exciting chapter for the club. We are sure our fans will give us their usual fantastic support as we aim to bring them more and more success and continue to make Celtic a club they can be proud of."
Lennon guided the club to three league titles and two Scottish Cups during his time in charge.