Pozuelo became the club's third - and highest profile - signing of the day after they earlier confirmed the arrival of teenagers Gregor Zabret and Alex Gogic.
He has signed a three-year deal at the Liberty Stadium.
Pozuelo, who made 11 senior appearances for Betis last term and becomes the Swansea's seventh Spanish players, will join the club on their 10-day tour of Holland.
"Since I've been a little boy it has been my dream to play in the Premier League. I am very happy to have joined Swansea City," he told the club's official website.
"From the moment I heard of the interest from Swansea I have watched their games and followed the news at the club.
"The style of the team suits me, and so too does the style of the manager. Of course, there are a lot of Spanish players here including my old Betis team-mate Jose Canas, and that will help me to settle quickly.
"I am looking to improve my English immediately as I want to communicate better with my team-mates. On the pitch I just want to give everything I have to the club in order to help the team this season."
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