The young Norwegian cut an assured, composed figure as he was presented at a media conference and shown off to hundreds of fans who turned up outside the stadium at lunchtime yesterday.
Deila, 38, the shock appointment who agreed a 12-month rolling contract, will appoint an assistant manager in the coming days and former Celtic and Scotland midfielder John Collins is the frontrunner.
All eyes were on the new man yesterday as he took questions from around 40 reporters and admitted he faced a huge step up after leaving the smaller Norwegian champions, Stromsgodset, for Celtic.
His predecessor, Neil Lennon, had revealed yesterday that Deila was considered by Celtic for the assistant manager's job when Johan Mjallby left the club at the end of the season, only for him to end up in the biggest position of all only a few weeks later.
Deila said his commitment to attacking football at Stromsgodset would continue at Celtic and that the big difference between the clubs was the far greater support, noise and atmosphere he would encounter at Parkhead.
"I can't say how I'm going to react to that but I know I am a quick learner and that's the most important thing. You have to learn from experiences, and develop, and that's what I want.
"I have to be humble. You can ask me questions about Europe [qualifying for the Champions League] - can I deal with it? - we'll see. I just have to look around me and use my energy on the most important thing and that's the product, what's happening on the pitch. If the product is good then good things will come from that.
"I'm stunned, of course, it is unbelievably big and it makes me very proud but also very, very energised. I'm looking forward to working with the boys and the staff and doing something to perform out there with the boys so that the crowd and the fans are happy."
Deila was flanked by chief executive Peter Lawwell throughout his media dealings at Parkhead. At one point he was asked what he had needed to hear the most from Lawwell during this week's discussions. "That I was wanted. Everyone is the same. If you don't feel wanted you don't feel safe, and if you don't feel safe you don't do the best job. That's the same for the players, they have to feel that I believe in them and that I really want them. That's what Peter has given me and that's why I sit here with good confidence now. That's important."
"I had a very good meeting with [major shareholder] Dermot Desmond too. He sees things. I could have left the room after three minutes because he had already read me. He has an unbelievable knowledge and I know how he has put things together. I have big respect for him."
There was a moment of humour when Deila was asked about the photographs which were appeared in the newspapers and online this week, showing him stripping to his underpants and throwing his clothes into the crowd after a crucial Stromsgodset win in 2009.
"That bet was between the fans and me," he said. "But the pictures were not so good, I felt they could have a better angle!" When asked if he might ever strip after a Celtic result, he laughed and said: "If we win the Champions League . . ."