Collins has begun his role as Celtic assistant manager after being named as Ronnie Deila's right-hand man earlier in the week.
The appointment raised questions about Collins' relationship with Brown, who was a Hibs player when the bulk of the first-team squad lobbied chairman Rod Petrie with grievances about the approach of then manager Collins during an infamous meeting in early 2007.
Collins soon led Hibs to the League Cup and Brown left for Celtic in a £4.4million move in the summer, and the former Scotland midfielder has no issues with the club captain.
"I worked with Scott at Hibs on the training pitch and he was a fantastic professional and an excellent player," Collins said at Celtic's Lennoxtown training ground.
"Gordon Strachan asked me at the time about Scott coming to Celtic and I told Gordon he would be a wonderful signing for Celtic. I was proved right. He has been the captain, playing terrifically well, and an international.
"I'm looking forward to seeing Scott next week and working with him.
"I had a terrific relationship with Scott on the training pitch and never had one problem with him ever.
"Why? Because he's a good professional who loves training and likes performing well. And he did perform very well for me at Hibs, week in, week out, and that's one of the reasons he got his big move to Celtic."