Manchester United have agreed to sell Angel Di Maria to Paris St Germain for 63million euros.
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.
Pozuelo is the third Spaniard to sign for Swansea in the past week, joining former Betis team-mate Jose Canas and Jordi Amat from Espanyol.
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 tomorrow 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."
While Pozuelo is likely to go straight into first-team contention, 17-year-old goalkeeper Zabret and 19-year-old midfielder Gogic are more likely to be players for the future.
Zabret joins on a two-year deal from Slovenian side NK Domzale while Cyriot Gogic agreed one-year contract having left Olympiakos on a free transfer.
Zabret said: "I'm very happy to be here. It is a great environment for me to develop and I'm looking forward to starting work.
"There are some great people at the club and I hope to get as much training with the first team as possible to help my development."
Gogic added: "I was very impressed with what I saw when I came here on trial and I'm delighted to have signed for Swansea."