The 25-year-old has been with Mark Hughes's side for four years, making 67 appearances in all competitions, but found game time hard to come by last season and was restricted to just 11 outings in the Premier League.
The deal with the newly-promoted Spanish side is thought to include a clause allowing them to make the move permanent next summer should they remain in the top flight.
Writing on Twitter after the announcement, Muniesa said: "It's hard to say goodbye. After four years, I leave my second home, a great club that gave me the opportunity to play in the Premier League and achieve some of my friends.
"I leave a lot of friends. Thanks to all the staff, all my teammates during these seasons and people who work for Stoke. Special mention to the supporters, you make me feel so proud to play for you and Stoke will always be in my heart.
"Best of luck for the future! I'm a Potter for life! Goaaarn Stoke!"
Muniesa joined Stoke on a free from Barcelona in July 2013.