The 31-year old's contract ends with the Seagulls on July 1 and he has since rejected a new contract to sign a three-year deal with the Midlands club.
Stockdale made 45 apperances for Brighton last season, helping guide them to promotion after finishing second in the table.
The former Fulham keeper moved to Brighton in 2014 and went on to make 139 appearances for the south coast club.
OFFICIAL: We're delighted to announce that David Stockdale has become Harry Redknapp's first signing as Blues boss. #BCFCpic.twitter.com/ArqVhOvepT
— Birmingham City FC (@BCFC) June 13, 2017