The centre half was targeted by Alex McLeish after attempts to sign Cardiff's Roger Johnson failed.
City have accepted a £4m fee (although as usual, both clubs are reporting the fee as "undisclosed") for the defender who agreed terms today at St Andrews.
There has been no news as to whether the fee paid by Birmingham includes a sell on clause plus money if a certain amount of appearances are reached
Dann made 49 appearances for City and scored four goals.