The 38-year-old arrives from Stromsgodset, who he guided to the Norwegian Tippeligaen title last season.
Delia also won the Norwegian Cup with his former club in 2010.
“It is a magnificent honour to be named the new manager of Celtic, 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,” Deila told the club’s official website.
“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."
Celtic had held talks with Roy Keane but the 42-year-old opted to remain Republic of Ireland assistant coach. The Scottish club were also reportedly interested in speaking to Henrik Larsson, who currently manages Falkenberg.
Celtic’s chief executive Peter Lawwell believes Deila’s attacking style of football will win over fans at the club.
"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,” said Lawwell.
“Knowing that he was so highly-rated across Europe, Ronny was one of the first candidates we considered as manager and having discussed the opportunity with him at length, we are convinced he has the talent and the determination to deliver very positive results for the club and our supporters.
“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.”