The Spain Under-21 international arrives on a free transfer after his contract with the Liga champions expired and becomes Potters boss Mark Hughes' second recruit
The centre-back was part of the Spain squad that won the summer's European Under-21 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 his new 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.
"My season only finished a fortnight ago when the European Championship ended but I can't wait to get started for Stoke. I would start tomorrow if the club asked me to."
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."
Muniesa, a product of La Masia, made just two appearances for Barcelona's senior side during his time in Catalunya.