The 24-year-old has arrived for an undisclosed fee, becoming the fourth signing the club has made in the January transfer window.
City, managed by Lee Bowyer, have also secured Teden Mengi, Taylor Richards, and Onel Hernandez on loan.
After securing the move, Bacuna told BluesTV: "It is nice to be here, [I am] excited to get going.
"I have got the opportunity to play games and show my abilities - Birmingham is a nice city. It is a big club and I am really excited to be here.
"The most important thing is to build something with the team and the Club. I have got three-and-a-half years to do it, I am going to do everything to make it an incredible time."
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