The Wales international moves to St Andrews on a season-long loan.
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The 19-year-old spent last season on loan at fellow Championship side Stoke, scoring six goals in 49 games.
Koumas told Birmingham's website: "Just how big of a club this is, how passionate the fans are, the project that I've heard about and after speaking to the gaffer, there was no other way about it - I was coming to Birmingham.
"I want to be wanted by a manager and I know he knows a lot about me. It's always about developing and wanting to get better but I'm also here to come and prove what I can do, score goals and get assists."