The 38-year-old was unveiled at a press conference at Celtic Park on Friday after signing a 12-month rolling contract, fresh from guiding Stromsgodset to the league title in Norway last season.
Deila, who also managed Stromsgodset to the Norwegian Cup in 2010 following a three-year spell with the south Norway side as a player, insisted the lure of Celtic was too much to resist.
"It was a very easy decision," Deila said.
"I'm very proud today. It's been a fantastic day and I felt this was the right move for me now after nine fantastic years at Stromsgodset.
"It's a fantastic step and I think this is the right step for me now. I feel very confident and comfortable.
"I feel this is like a family and I feel at home with a lot of the values at this club.
"It's gone very quick (the interview and selection process). When I heard the name (Celtic) of course I was very interested at once because in my stomach I felt this was the right move for me."
Deila paid tribute to the work Lennon did during his four-year tenure as Celtic manager and promised to deliver an attacking brand of football for the club's supporters.
"Neil Lennon has done a fantastic job here and of course I have to do a lot of the same things that he has and do some of the positive things," Deila said.
"My philosophy is first of all that I want to play offensive football. I want to have the game under control with the ball.
"We want to have possession and create chances and especially in the home games we want to give the fans entertaining football. Other than that I am here to win trophies - that is what the club is for.
"To do that we need to develop players and the staff of course. Everybody in the staff and the team need to progress and if we do that we can achieve good things."
Celtic chief executive Peter Lawwell added: "I'm delighted to announce Ronny Deila as our new manager. We've had a very thorough interview process and we've seen a lot of outstanding candidates but Ronny was the most outstanding.
"We're delighted to have attracted him here to Celtic. He's the right man because he is intelligent and he's progressive.
"He's modern. He's got a fantastic track record in terms of winning and developing players. He fits probably perfectly where we sit as a club - his credentials are ideal for Celtic."
Lawwell also confirmed there is more than one name in the frame for the assistant manager's vacancy and said that process would intensify next week.
Deila was asked if former Celtic and Monaco midfielder John Collins was in the frame for the role as his assistant to which he replied: "Yes, he is one of them."