The Norwegian was named as Neil Lennon's successor and will begin life in the Parkhead dugout when the Hoops face KR Reykjavik in the Champions League second qualifying round early next month.
Deila arrives in Glasgow with a burgeoning reputation as one of the brightest coaches in the game and former Rosenborg star Lustig is delighted with the appointment.
He said: "He liked to play on the ground, attacking football, a lot of combinations, and when we faced them (Stromsgodset) at home, I found it really hard to beat them.
"I never won against them when they were at home. They played great football and I heard he was really good with the young lads. He is probably the most exciting manager in Scandinavia right now so I'm really happy to work with him."
Deila led Stromsgodset to the Norwegian league title last year and said an emotional farewell to his former club before beginning work at Parkhead.
Celtic are bidding for a fourth straight Premiership crown in his first campaign in the dugout and Lustig reckons there is a bright future in green and white.
He said: "Stromsgodset is quite a small team in Norway, they don't have the money of the big clubs. So that (winning the league) was a real achievement.
"They won the league last year, but the year before that they were at the top as well, so it wasn't a shock that they won the league. They have played really good football for some years now.
"He is really good with the young lads. Stefan (Johansen) is just one guy who has done really well, some other guys went to France as well.
"Maybe Celtic don't have as much money to buy players who are really good right now, so if he is going to develop the young lads, that will help us."
It was to prove a season of mixed fortunes for Lustig last time out as he lifted the Premiership crown but missed several months of the campaign through injury.
The Swede has put pen to paper on a new three-year deal to keep him at Celtic Park, and said: "I really love to play for this club so it was never a hard choice.
"I can play in Europe every year, the fans are amazing, and if I want to change clubs I will need to pick a smaller club. Maybe more money, but it's going to be a smaller club. I'm not that good to choose a bigger club than Celtic.
"And my family really love it here as well so it was never a hard choice."