The 21-year-old arrives for a nominal fee despite his contract expiring in Andalusia due to being under the age of 24.
Pozueo becomes the third Spanish player to join the club since July 1 following the arrivals of his ex-Betis team-mate Jose Canas and Jordi Amat from Espanyol.
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"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."
On a busy day of transfer activity at the Welsh club, boss Michael Laudrup also strengthened his side with the captures of promising youngsters Gregor Zabret and Alex Gogic.
Slovenian goalkeeper Zabret, 17, has arrived from Domzale, while 19-year-old midfielder Gogic - a Cyprus Under-19 international - has signed from Greek side Olympiakos.
Gogic has signed a one-year contract on a free transfer, while Zabret joins on a two-year deal for an undisclosed fee.
Leaving the club, albeit temporarily, is defender Kyle Bartley, who has agreed a season-long loan with Championship side Birmingham.