The 31-year-old was a key-man in Brighton & Hove Albion’s promotion to the Premier League last season.
He made 45 appearances and conceded just 40 goals - keeping 22 clean sheets process - in their historic season which saw them finishes runners-up in the Championship.
But the soon-to-be out-of-contract stopper will not remain with the Seagulls as they step up to the top flight, opting instead to sign a three-year deal with the Championship outfit.
He will link up with Harry Redknapp as the former Spurs boss’ first signing when he join Blues on a free transfer on July 1 - when his Albion contract expires.
Having already been offered a new deal at the Amex over the summer, there has been plenty speculation of the popular Leeds-born keeper’s future.
He was linked to his hometown club Leeds United as well as Premier League giants Chelsea among other.
Albion boss Chris Hughton, speaking to the club website, said: “Firstly, and most importantly, I would like to thank David Stockdale for his immense contribution over the past three seasons.
“He has been the stand-out goalkeeper in the Championship, and was a key member of our side as we went so close in 2016 and when we won promotion last season.
“There were some truly remarkable and very memorable moments, not least those three vital penalty saves last season against Fulham, Brentford and Sheffield Wednesday - all of which will live long in the memory for us all.”
Stockdale is expected to become Blues’ first choice goalkeeper with over ex-Albion man Tomasz Kuszczak and Adam Legzdins, who recently signed a new deal.