The former Hibs head coach has signed a 12-month rolling contract to succeed Brendan Rodgers in the Parkhead hotseat.
Lennon previously took charge of the Bhoys between 2010 and 2014, leading the side to three league titles and two Scottish Cups.
The former Northern Ireland international will be assisted by John Kennedy, with former Chelsea and Fulham winger Damien Duff continuing as first-team coach.
Speaking to Celtic's official website, Lennon said it was a "massive honour" to take the reins at Parkhead, adding: "I had always dreamed of returning to this role on a permanent basis and I am absolutely delighted to once again be part of one of the biggest and best clubs in the world - an institution which really does mean so much to me and one which has always been such a huge part of my life.
“When I was asked to take over in February, I felt it was my duty to do so. Celtic will always be my club and I wanted to help finish the job which had been started.
“I was delighted with the way the players stuck to their task and delivered another historic success, which is unlikely to ever be repeated.
"I was also delighted to receive such great support from our fans since returning, something for which I will be forever grateful."
Celtic chief executive Peter Lawwell added: "We’re delighted to name Neil as our new manager. Neil stepped up to the plate and answered our call in February, and in the difficult circumstances, played a huge part in delivering the treble to Celtic.
“We have known Neil as a player, captain, coach and manager. He has brought great success to Celtic in the past and we’re sure he’ll do so again in the future.
"He’s a Celtic man, a winner and someone we’re delighted again to have as part of the club.
“Neil has a great record in identifying players, and he has already been working hard in this area as we look to strengthen the squad this summer. We’re all looking forward to a positive future together.”