The 23-year-old Swiss international winger has signed a five-year contract with the Potters and will link-up with his new teammates this week ahead of Saturday's trip to Tottenham.
Shaqiri, who has scored 17 goals in 46 appearances for Switzerland, was a member of the Bayern Munich squad that won the 2012/13 European Champions League.
Chief Executive Tony Scholes said: "It's no secret that we have been pursuing Xherdan for some time now and we are delighted to have finally secured his signature.
"He's an exciting young player who is really looking forward to playing in the Premier League having played at the very highest level in Germany with Bayern Munich and in Italy with Inter.
"Xherdan will be a fantastic addition to our squad and adds to the attacking options at the manager's disposal."
Manager Mark Hughes said: "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 has been allocated number 22 for the 2015/16 Barclays Premier League campaign.
Tickets for Shaqiri's potential Britannia Stadium debut against West Bromwich Albion later this month are on sale.
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