The 38-year-old arrives from Norwegian outfit Stromsgodset, where he won the domestic league in 2013, as well as the Norwegian Cup three years earlier.
Former Celtic midfielder Roy Keane had been tipped to make a return to the club, but the Republic of Ireland assistant withdrew from talks on Monday.
Deila will attempt to fill the boots of Lennon, a legend at Celtic Park, who won five Scottish Premier League titles as a player, before guiding the club to three consecutive crowns in the past three seasons.
"It is a magnificent honour to be named the new manager of Celtic," Deila told the club's official website. "One of the world’s great football clubs and a club I have such enormous respect for. I will treasure this opportunity and will give everything I have to achieve success for Celtic and our wonderful fans.
"I know what I want for Celtic and our supporters and that is the best of everything, it is what our fans deserve.
"I want to deliver the best attacking, exciting and entertaining football we can play, for the players to give their best every time they take to the field of and, of course. I want my players to work with me to achieve the best results possible and bring trophies to Celtic.
"Celtic is in great shape and the club has enjoyed real success in recent years due to the hard work of Neil and his team. I want to carry on this work and continue to bring happy times to Celtic. I can’t wait to get started on this journey."
Chief executive Peter Lawwell, meanwhile, pointed to Deila's philosophy as one of the primary reasons for offering him the job.
"We believe Ronny will prove to be a fresh and dynamic new manager and someone who will give us a bright and energetic way forward for Celtic," he said.
"Ronny likes to play attacking, winning football, the Celtic way, something I know our supporters will endorse.
"As the new season begins, I am sure our fans will get right behind Ronny and the players once again as we aim to bring success to Celtic and continue to deliver a club they can be proud of."
