The French defender, 26, was a free agent after his contract with Wolves was terminated by mutual consent in January and was handed a one-year deal by the Parkhead club after impressing on trial during their pre-season trip to Germany and Austria.
Mouyokolo will play in Celtic's challenge match against Brentford in London tomorrow but when the competitive action resumes he will have to get past regular centre-backs Kelvin Wilson and Efe Ambrose as well as another of Neil Lennon's summer signings, Virgil Van Dijk.
The former Boulogne and Hull City player said: "The competition is very important at big clubs.
"As long as the competition is fair and someone doesn't stick it to you.
"Sometimes it happens but not from what I have seen here.
"I get on with everybody, with Kelvin and Virgil, who came in at the same time as me.
"It is a good crowd, good people.
"But sometimes at clubs, defenders don't like each other.
"I have been playing with players and you don't like each other and that makes it hard to play.
"I will work hard to get a place in the starting 11 but as long as the competition is really fair that will help the club and help us as well.
"When he plays I expect him to do well and hopefully when I play he expects me to do well.
"That is a team. We work together, we work for the club and not for ourselves."
Mouyokolo's delight at joining the Scottish champions is all the more sweet after taking the "risky" decision to leave Wolves when he still had 18 months left on his contract.
"Everybody was asking me what I was doing," he said.
"It is very risky when you have one-and-a-half years left on your contract.
"I would say most other players would take the security and stay but I had trust in my physio and personal coach in France and I have been working really hard for three months.
"I would say I am more physical than technical
"I'm French but I'm not like Laurent Blanc.
"I like to defend with my head, try to think and read the game.
"In Scotland you sometimes have tough games so you have to be physical so I like to fight as well."