Although the 21-year-old's contract with Betis had run out, Swansea said on their website (www.swanseacity.net) they paid an undisclosed transfer fee.
He is the third Spanish player to join the Swans for next season following the arrivals of Jose Canas, also from Betis, and Jordi Amat from Espanyol.
Swansea, who finished ninth last season under Michael Laudrup, travel to the Netherlands on Wednesday for a 10-day pre-season tour.
Photograph: Marcelo del Pozo/Reuters