Shaqiri has signed a five-year contract at the Britannia Stadium.
The Switzerland international only joined Inter Milan in January this year from Bundesliga giants Bayern Munich.
“I am very happy, and incredibly excited that this transfer to Stoke City has finally happened,” he told the Stoke City official website on Tuesday.
“Over the past three days I have met great people at the club and witnessed the wonderful atmosphere at the Britannia Stadium on Sunday. That experience was overwhelming.
“My special thanks go to the manager, Mark Hughes, Chief Executive Tony Scholes and 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 teammates and make my debut for the Club. It feels great to finally be a Potter!”
