The 21-year-old, who was a member of the Spain squad that recently won the European Under-21 Championship, has signed a four-year contract with the Potters.
He becomes manager Mark Hughes' second summer signing following the arrival of Erik Pieters from PSV Eindhoven.
"I'm very excited about moving to England to play for Stoke City and will do everything I can to help the club," Muniesa told the official Stoke 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."
Hughes said: "Marc has been well-schooled by Barca. Technically, he's a very good player and I've no doubts he will be an excellent addition to our squad.
"I know he's very highly-regarded in Spain and was attracting interest from clubs in La Liga, but he's an ambitious young man and wants to test himself in English football."
Muniesa has made three substitute appearances for the Barcelona first team and spent last season playing for their B side.
He has been capped five times by the Under-21s and has also represented his country at Under-16, 17 and 19 levels.