The Championship club accepted an undisclosed fee from the Potters for the 19-year-old, with the keeper set to stay at Birmingham on loan until the end of the season.
Butland had earlier rejected talks with Chelsea because of his desire to play regular first-team football and had also been linked with Liverpool, Fulham, Newcastle United and Manchester City in this window.
Butland joined the Birmingham academy aged 14 and made his first-team breakthrough this season after a successful loan at Cheltenham Town.
His rise through the ranks also saw him become England's youngest ever goalkeeper when he won his first senior cap in a friendly against Italy last August.
Both Everton and Southampton tried to sign the talented teenager last northern summer after he was called up to the England squad for EURO 2012 after third-choice goalkeeper John Ruddy broke his finger.Butland told Sky Sports News he decided to move to Stoke as it 'ticked all the boxes'.
He said: "I feel very good. I'm glad to get it done and it's the next step of my career and I'm looking forward to it.
"I tried not to get that in my head (about a move in this window) because anything can happen in football and I decided just see what came of it.
"I feel very lucky to come to a great club. It just ticked all the boxes for me.
"I've come to a solid club who are doing well in the Premier League with great fans. The staff around the club, the goalie coach and the manager, I can see it is a very professional environment and I am looking forward to getting to work with them."
Stoke manager Tony Pulis said of the deal: "This is a fantastic signing for the club because Jack is the best young keeper in the country with an outstanding future ahead of him in the game and we are delighted to bring him here.
"It is important that we build for the future and this adds to the strong nucleus of young players which we have within the squad. Both this signing and the arrival of Brek Shea are significant long term investments."
It was the last piece of business of the transfer window for the Potters, who also completed the signing of FC Dallas winger Brek Shea for £2.5 million ($3.8 million), with Matthew Upson leaving on loan to Championship side Brighton & Hove Albion and Rory Delap moving to Barnsley on loan.
Earlier, Pulis travelled to Wembley to help secure Shea's work permit in a bid to complete the deal.
Pulis said of Shea's capture: "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."
Speaking of Upson's departure, Pulis said: "Matty has been a fantastic professional throughout his time here and an influential figure in the dressing room.
"He now has a chance to play some regular first-team football. It's a great opportunity for both Matty and Brighton, so we wish him all the best."