The 21-year-old's arrival means Swansea now have seven Spaniards on their books, and Pozuelo told the club's official website: "That will help me to settle quickly.
"I am very happy to have joined Swansea City. Since I've been a little boy it has been my dream to play in the Premier League.
"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.
"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."
Pozuelo made 11 league appearances for Betis last season, and his arrival is unlikely to be the last at the Liberty Stadium this summer.
Jose Canas and Jordi Amat have already been brought in, and chairman Huw Jenkins has admitted an interest in Lyon striker Bafetimbi Gomis, Wilfried Bony of Vitesse Arnhem and Liverpool's Jonjo Shelvey.