The former Newcastle United stopper joins Birmingham on a free transfer.
"I coached Dave when he was a young player at Newcastle and I was the reserve manager," said Clark.
"He's a good professional with a strong character and has leadership qualities.
"His versatility is important to us in the way that we want to work.
"I think we've done really well to get him because he played a huge part in what Burnley did last year.
"When I spoke to Sean Dyche he was really fulsome in his praise of what Dave had done."
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