The Norwegian previously shed his clothes in front of his home fans, in sub-zero temperatures after his side beat relegation in 2009.
Stromsgodset pulled off the feat on the final day of the season and Deila was true to his word, stripping off and throwing his clothes into the crowd amid the celebrations.
At his first Parkhead press conference, he said yesterday: "That bet was between the fans and me, but the pictures were not so good as I felt they could have a better angle."
Asked if would show his cheeky side again, the 38-year-old said: "If we win the Champions League."
Highly-rated Deila guided Stromsgodset to a Norwegian Premier League title win in 2013.
As first revealed by the Evening Times, Deila has been named as the new manager, on a 12-month rolling contract, replacing Neil Lennon.
He was mobbed by Hoops fans as he was presented to supporters yesterday afternoon.
Crowds followed him, taking pictures and asking for autographs, as the new Parkhead boss took his first walk along the Celtic Way.
Among those who waited hours in the blistering sun to see him were Conor Cawley, 16, and Chris Eadie, 17, from Glasgow.
Chris said: "Usually the job goes to someone in the Celtic family, but I'm happy with Deila.
"I think choosing someone totally different and unexpected makes it all a bit more exciting.
"I'm glad we've got a European manager, that's exactly what we need right now."
Meanwhile, Conor was more cautious, adding: "We need to give him a chance, but I'm pretty happy with the decision."
Hoops fan Liam Kirkbride firmly believes Deila is the right man for the Parkhead hotseat.
The 38-year-old said: "A lot of people are saying we don't know him, or know anything about him.
"But that's what we said about Henrik Larsson, and look how that turned out, you never know what will happen.
"It was the same with Wanyama, nobody knew who he was when he arrived here, but he turned out great, and we sold him for £12million.
"We just have to look at what Deila has done in Norway and give him a chance here."
Before walking down the Celtic Way, the Norwegian posed for pictures in the shadow of Celtic legend Jock Stein's statue.
Deila said: "I will treasure this opportunity and will give everything I have to achieve success for Celtic.
"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 know what I want for Celtic and our supporters and that is the best of everything, it is what our fans deserve."
Barry Keegan, 48, from Paisley, said: "I think we've made the right decision. He talks about attacking football and that's what we want at Celtic."
The Evening Times broke the news of Deila's arrival at Parkhead yesterday morning.
Celtic chief executive Peter Lawwell said: "Ronny likes to play attacking, winning football, the Celtic way, something I know our supporters will endorse.
"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.
"Knowing that he was so highly-rated across Europe, Ronny was one of the first candidates we considered as manager."
Earlier this week, Roy Keane ruled himself out of the running to be manager.
The 42-year-old pledged to continue in his role as Republic of Ireland assistant coach after informal talks with the club.