Collins spent six years as a player at the Parkhead club during which time he became a hero to the Hoops support.
Since hanging up his boots he has spent spells in charge at Hibs – where he won the League Cup in 2007 – and Charleroi in Belgium.
The former Scotland midfielder, who scored against Brazil in the national team’s last appearance in the World Cup finals at France 1998, also had a stint at Livingston.
He was Director of Football at the West Lothian club and was widely praised for the standard and style of football the team produced in his time there.
In recent months he has been working as an SFA coach, but his appointment as No.2 to Ronny Deila has come as something of a surprise.
Hoops captain Brown was part of an alleged players’ revolt when Collins was in charge at Hibs and there have been doubts expressed about whether the two men can work together.
But former Monaco, Fulham and Everton star Collins insisted he is relishing the opportunity of teaming up with Brown once again.
He said: “Scott Brown is a fantastic professional and an excellent player. When Gordon Strachan asked me about Scott coming to Celtic I told him he would be a wonderful signing for them. I was proved right.
“He has become the club captain and has done well for the club. I am looking forward to seeing Scott when the players come back to training next week.
“I had a terrific relationship with Scott on the training pitch. I never had a problem with him ever. Why? Because he likes training and is a great player and a great professional.
“What happened at Hibs was a long time ago. What happened at Hibs seven years ago is in the past and I am looking forward to starting at Celtic.”
Asked what he had learned from his turbulent spell at the helm at Hibs, Collins said: “You learn to expect the unexpected. I was surprised. It shouldn’t have happened.”
Collins admitted he is looking forward to working with Norwegian coach Deila and helping Celtic to qualify for the group stages of the Champions League.
He said: “I am sure Ronny will ask my opinion on football matters. I will be there to give an opinion every day and every week.
“I won’t be picking the team, that’s the manager’s job. But I will still be working hard on the training pitch. I am an assistant now and am looking forward to it.
“I met Ronny two weeks ago and we had a long chat. We have a similar football philosophy. It was very important for me to work with somebody who had similar ideas to myself.
“We have big, high pressure games coming up soon in the Champions League qualifying rounds. We have to hit the ground running and I am sure that we will be able to do that.”