Legzdins slipped down the pecking order at Brum earlier this summer after Harry Redknapp successfully convinced David Stockdale to reject a new contract with Brighton and make the move to the midlands.
Burnley meanwhile have been on the look out for a back-up goalkeeper after Paul Robinson hung up his gloves at the end of last season.
30-year-old Legzdins has signed a three-year deal at Turf Moor and will compete with tom Heaton and Nick Pope for the No 1 jersey.
Legzdins told Burnley's club website: “Interest from someone like Burnley is something you can’t ignore, no matter what the situation was at Birmingham, and after speaking to the people here I think it will be a really good fit for myself.
“I’m looking forward to working hard to see what happens. I’m looking forward to working with the goalkeepers that are already here.
“Tom has achieved fantastic things. I have played against him in the Championship many times and Nick Pope is a great talent behind him.
“But I’m here to excel and I want to push them and help improve the goalkeeper department.
“I think I can add a lot of things which can help us all kick on and I’m looking forward to learning from Billy and the other two goalkeepers.
“To be in an environment where there is healthy competition can only help us all moving forward and I want to achieve as much as possible.
“Looking at the fixtures coming up, it’s nothing but excitement for me and my family.”
SIGNING: We are delighted to announce the signing of Birmingham City goalkeeper Adam Legzdins.
— Burnley FC (@BurnleyOfficial) August 8, 2017
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