The 21-year-old, who left the Catalan outfit at the end of last season, has revealed that he is "very excited" to join the Potters.
"I'm very excited about moving to England to play for Stoke City and will do everything I can to help the club," he told the club's official website.
"It wasn't a big decision for me to make. I came to England yesterday to meet the people at the club and look around the training ground, which is very impressive.
"My season only finished a fortnight ago when the European Championships ended, but I can't wait to get started for Stoke. I would start tomorrow if the club asked me to."
Muniesa, who has signed a four-year contract, had previously been linked with a number of European clubs.