Shaqiri, who was spotted at the Britannia Stadium when the Potters lost 1-0 to Liverpool yesterday, has penned a five-year deal with Mark Hughes's side.
The 23-year-old could make his Premier League debut against Tottenham Hotspur at White Hart Lane on Saturday.
"I am very happy, and incredibly excited that this transfer to Stoke City has finally happened," he told the club's official website.
"Over the past three days I have met great people at the club and witnessed the wonderful atmosphere at the Britannia Stadium on Sunday [against Liverpool]. That experience was overwhelming.
"My special thanks go to the manager, Mark Hughes, chief executive Tony Scholes and [technical director] Mark Cartwright for their work in helping to make this deal happen over the past few months.
"I sincerely appreciate it so much, and will give my utmost to pay them and the supporters back on the pitch over the coming months and years.
"I can't wait to meet my new team-mates and make my debut for the club. It feels great to finally be a Potter!"
Manager Hughes added: “He’s a dynamic and explosive player who will bring something different to the group and at the age of 23 he still has a great deal of potential.
“In the chats I’ve had with him it’s obvious that he’s excited about playing in the Premier League and showing what he’s capable of.”
Shaqiri won the Bundesliga twice and the Champions League once with Bayern Munich before joining Inter in January.