Butland spent a large part of deadline day at the Britannia Stadium tying up the details of his move, which will see him return to St Andrew's on loan until the summer.
Birmingham's terrible financial situation has forced the Championship club to put their entire first-team squad up for sale and Butland was always likely to attract interest.
The 19-year-old, who has one cap for England, turned down the chance to talk to Chelsea on Wednesday as he is seeking regular first-team football.
Stoke's current number one Asmir Begovic is said to be a target for Manchester United in the summer.
Shea arrives at the Britannia Stadium subject to international clearance after manager Tony Pulis travelled to London to secure a work permit for the 22-year-old.
The American has signed a four-and-a-half year contract.
Pulis said: “It’s fantastic news that we have been able to push through the deal.
"Brek is a very, very exciting player, and one who we firmly believe could go on to become an outstanding player for this football club.
"He has terrific pace, a very good left foot and is capable of scoring goals. He has all the tools needed to be a success here."
Peter Crouch's prospective move to QPR fell through, while Rory Delap has confirmed a loan move to Barnsley until the end of the season.