The club captain was forced to pull out of the Scotland squad for the 1-0 World Cup qualifier victory in Croatia at the start of June through injury.
Celtic manager Neil Lennon gave the former Hibernian player extra time off to recover but Brown says he is now back and raring to go.
He told the club's official website: "I'm only back one day and I've not trained with the squad, I'm doing my own running.
"I feel not too bad. I've not really done twisting and turning and passing the ball yet so I'm a bit behind everyone else, but I'll catch up soon.
"My pre-season won't be much different from everyone else's. I'm just playing catch-up because they were in a week earlier than me. I'll hopefully join in with a few games here and there.
"I'd love to play in pretty much most of the games but we'll have to see how I go in training and how far behind my touch is from everyone else. My body feels fine, I feel good from the four weeks of recovery and it's been good to just rest."
Celtic face a crucial Champions League second qualifying round double header with Northern Irish champions Cliftonville next month and Brown is under no illusions about the importance of the tie to the club's aspirations for the new season.
"It's been short and sweet but it's been good to get back in and see the lads," he continued. "We've not had the longest break ever but for me, I enjoy coming back and seeing the lads.
"I enjoy training and playing football, it's more a hobby than a job for us. We're all feeling quite refreshed and pre-season won't be as tough as it would be if we had seven or eight weeks off. We've got a lot of games as well so we'll get our match sharpness back quickly.
"The Cliftonville tie is going to be huge. It will be two good games and we have to try and get everyone fit and ready. It will be hard with some players still away on international duty.
"It's hard to get everyone back into the squad on time but I'm sure the gaffer will do that. It will help us for the start of the season as well but it will be hard and we just have to get through it."
Brown's return to Celtic's Lennoxtown training base saw him meet the club's two summer signings Virgil van Dijk and Amido Balde for the first time and the skipper is looking forward to getting to know them on the pitch.
"The new lads seem friendly and it's good to have them in," he said. "Look at the size of them. It's good to have some height in the team, we've maybe missed that.
"They seem lively around the training ground and that's the main thing. There are a lot of games before the qualifiers so that will help us get used to how they play."