The 38-year-old former captain has been the subject of speculation for weeks and fans have welcomed the news that the uncertainty is set to finally come to an end.
"It was dragging on and it was meant to be last week or the week before," said Alan Horne, president of the Affiliation of Celtic Supporters Clubs. "Now it's resolved and the job at hand is to get the league flag back.
"He had one blip – the obvious one against Ross County in the Scottish Cup – but he won all eight league games, including beating Rangers at Celtic Park so his record is certainly good in that sense."
Former captain Lennon took over the helm in a caretaker capacity when Tony Mowbray parted company with Celtic after just nine months in March.
Hopes of landing the post long-term were initially dealt a blow following a shock 2-0 Scottish Cup exit to Irn-Bru First Division side Ross County. But an impressive recovery saw Celtic win all their SPL matches under Lennon to place him firmly in the frame for the job.
Lennon joined Celtic in a 5.75million move from Leicester in December 2000 and spent seven years in the east end of Glasgow, before spells with Nottingham Forest and Wycombe.
He returned to Parkhead in a coaching capacity in April 2008, before being put in charge of the reserves following Mowbray's appointment the following year.
Lennon is set to be assisted in his new role by Johan Mjallby, Alan Thompson and Garry Parker.
"He is certainly a fans' favourite," added Horne. "He's got a passion for the club and he has desire and hunger and a will to win. I think he will be a great appointment.
"You will always get people who think he is not experienced enough to manage at that level but give him a chance. He is very animated on the touch-line, which was certainly lacking in the last manager.
"The fight on and off the park last year was pretty poor and I think Neil Lennon has instilled that back in the team."