The 19-year-old goalkeeper has agreed a four-and-a-half-year contract with the Premier League side, but will be loaned back to Birmingham for the remainder of the season.
"It's been an incredible day - a very exciting one, but I'm glad it's finished. I love playing and I don't want to sit on the bench," Butland told BBC Sport.
"For me, it was important I went to a club where I can play and develop my game.
"I've got unfinished business [at Birmingham] and I want to help them this season. They have been very good to me."
Butland, who had been linked with clubs including Liverpool, Newcastle United and Manchester City, played for Team GB during the London 2012 Olympics.
He earned his first England cap in the 2-1 win over Italy in August.