The Scottish Premiership champions were forced to look for a new boss following last month's departure of Neil Lennon, who is seeking a new challenge after four years at Parkhead.
A number of candidates were linked with the vacant role, including former player Roy Keane and ex-West Brom boss Steve Clarke, but the Hoops have opted for Deila, a little known Norwegian.
The 38-year-old guided Stromsgodset to their first title in 43 years last season and chief executive Peter Lawwell is confident he will endear himself to the fans with an attacking brand of football.
"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.
"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."
Deila has vowed to continue the progress under former manager Lennon, who steered Celtic to the last 16 of the UEFA Champions League and a third successive title.
He said: "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.
"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."