The deal is worth just under £5million to Birmingham, who will keep the 19-year-old on loan until the end of the season.
That arrangement will suit Butland, who turned down the chance to talk to Chelsea earlier this month because he wants first-team football.
Stoke's current No 1 is Asmir Begovic, while the experienced Thomas Sorensen is also on the club's books.
Begovic has been linked with Manchester United and Chelsea but told Sky Sports News on deadline day he expects to stay at the Britannia Stadium until the end of the season.
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