The England Under-21 international has signed a four-year deal at the Reebok Stadium.
Muamba said, "I spoke to the manager and he revealed his plans for the club.
"I am very excited and I want to be a part of it. It is a great set-up here and I am going to give my best for the club.
"I am very happy with the move and I am looking forward to the challenge. I had my first taste of The Premier League last year and I wanted more. As soon as I knew of the interest of Bolton Wanderers I was ready to come here.
"I had a good year in Birmingham but this is a new start for me and I am looking forward to it.
"I was surprised to see Bolton right down there last year but Bolton are a big club and have been in Europe before.
"I think we can do that - especially with the players we have here and the players the manager is trying to bring in.
"I play the same way I train and the fans will always see me giving my best. Hopefully, I can score more goals from midfield."