The 38-year-old Norwegian takes over from Neil Lennon, who left the Scottish champions two weeks ago after four years in charge.
Deila guided Stromsgodset to their first title in 43 years last season and won the Norwegian Cup in 2010.
Deila, expected to meet the media later today, spoke of the "magnificent honour" in being named boss at a club "I have such enormous respect for."
He said: "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."
Celtic chief executive Peter Lawwell is confident the Norwegian "will prove to be a fresh and dynamic new manager".
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."
Celtic chairman Ian Bankier added: "We are delighted to have secured Ronny as Celtic manager.
"He is a highly regarded individual and a man who we are confident will bring great success to Celtic.
"He is a forward thinking coach and manager with a progressive approach.
"The Celtic board will support Ronny fully and in every way and we look forward to working with him."
Source : PA
Source: PA