The Norwegian was appointed Neil Lennon's successor at Parkhead yesterday, arriving in Glasgow with a burgeoning reputation as a coach, and skipper Brown is hopeful ahead of the new era.
He said: "It's going to be exciting. It always is when a new manager comes in, and he'll bring his own philosophy.
"When you have a new manager at the start of the season you know he's going to focus on different points. He's going to have different aspects in training and games, and what he expects from us.
"It's ideal and he's a young manager. He's about the same age as Neil Lennon when he took over. It's a good thing to give someone young a chance.
"He's produced the goods in Norway by taking a side from just about nowhere to the top of the league, and that's great.
"He's not long out of football himself, he finished just a few years ago, so he'll know what we want to do and what he wants to do. I'm sure he'll focus as much as possible on getting the ball down and playing good, sharp, passing football.
"I think managers thrive off the kind of pressure that comes with being at Celtic. It'll be a great experience, especially that first time he walks out at Celtic Park and there are 60,000 fans there just to see him. He'll love every moment."
Deila has little time to evaluate his squad before Celtic's Champions League qualifiers, but the 38-year-old will link up with Stefan Johansen, who he worked with at previous club Stromsgodset.
Brown said: "He had Stefan over in Norway and we've already seen what a good player he is, and if he worked underneath him there, I'm sure he'll be wanting to take him to the next level here. I'm sure he'll know how to do that.
"It was myself, Stefan, Kris (Commons) and Charlie (Mulgrew) that was the midfield diamond for the majority of the games.
"When Stefan came in, you're not sure how he'd cope with the physical challenges, but he gets stuck in and that's what we love about him."