The Hoops returned to pre-season training on Tuesday as new Parkhead boss Ronny Deila put his squad through their paces for the first time.
And skipper Brown says the champions' hard work will pay off as the countdown continues to their clash with KR Reykjavik.
He said: "The main thing is that the new manager gets into it and sees how we are building up and how we are going to perform, and get the formation and team settled by then.
"Everyone is in good shape. The lads are pros and always keep themselves ticking over in the off-season.
"We get schedules of what we should be doing and what we shouldn't be doing and the lads have stuck to that well.
"The sports scientists focused on it and tried to get us all in tip-top shape for the new manager coming in."
Deila was assisted by new Hoops No.2 John Collins and coach John Kennedy as he took to the Lennoxtown pitches for the first time this week.
His decision to appoint Collins was a controversial one after he and several players, including Brown, had a bust-up while at Hibernian.
But the 29-year-old says there are no hard feelings between him and his former boss.
Brown said: "There will always be negatives here and there and people trying to stir it, but we have just got to focus on the positives.
"It is two good management staff that have come in and it is going to be good for us.
"He (Deila) phoned me and said who he was going to be bringing in. It has been good so far. It has been interesting.
"John has come in and everyone is making it a big issue, but me and John have got on fine, there have been no hard feelings whatsoever.
"It has all been positive and hopefully that continues.
"It is all about not falling out with people. You know that someone could come back around the corner and you could work with them again.
"I knew John might be working at Celtic at some point because he is a legend here. There was always that possibility."
With their first venture into Europe looming large on the horizon, it has been a short summer for Celtic as they get back down to business.
But Brown has kept himself busy during the close-season by starting a Uefa B Licence coaching course at Largs.
He said: "I think it's good for any professional to learn that aspect of the game, though.
"It shows you what goes on behind the scenes and that it's not about turning up and putting out cones.
"There is a lot of planning and a lot of thinking that goes into it."