The Spain Under-21s international arrives on a free transfer after his contract with the La Liga champions expired and becomes Potters boss Mark Hughes's second recruit
The centre-back was part of Spain Under-21s squad who won the summer's European Championship in Israel and becomes Mark Hughes's second signing since taking over from Tony Pulis, following the arrival of Erik Pieters from PSV.
The 21-year-old is delighted to have joined the Premier League outfit, telling the club's official website: "I'm very excited about moving to England to play for Stoke City and will do everything I can to help the club.
"It wasn't a big decision for me to make. I came to England [on Monday] to meet the people at the club and look around the training ground, which is very impressive.
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Hughes is confident that Muniesa will be a success in English football, stating: "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."
The Potters' chief executive, Tony Scholes, highlighted the key role that Hughes played in the deal.
"Marc has an excellent pedigree, as you would expect from someone who has come through the ranks at a club like Barcelona, and we're delighted to have secured his signature," he added.
"We were alerted to his availability and moved quickly to make him a Stoke City player. The whole process was greatly helped by Mark Hughes's links with Barcelona and it's clear to see he's very excited by the challenge of making an impact in the Premier League with us."