He succeeded Neil Lennon, who resigned at the end of the season after four years at the helm in which he won the Scottish Premier League in the last three of them.
"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," Deila said.
"I know what I want for Celtic and our supporters and that is the best of everything. I want to deliver the best attacking, exciting and entertaining football we can play.
"It was a very easy decision to join," he told a news conference. "It's a fantastic step for me and the right step for me now."
Celtic chief executive Peter Lawwell said Deila would prove to be a fresh and dynamic new manager.
"Knowing that he was so highly-rated across Europe, Ronny was one of the first candidates we considered as manager," he told a news conference.
"Our strategy is to develop our own players and find uncut diamonds and Ronny's credentials are ideal for that."
Lawwell said there were "three or four candidates" to become assistant manager and Deila confirmed that one of them was John Collins, the former Scottish international who played at Celtic from 1990-96 before joining AS Monaco, Everton and Fulham.
(Writing by Steve Tongue, editing by Ed Osmond)
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