Villalba made 17 appearances and scored one goal for BluesBCFC
The attacking midfielder's move is initially on loan with an option to buy at the season's end.
Villalba, 21, was brought in this summer by Blues on a free transfer from Valencia.
Having initially been a regular, Villalba has subsequently struggled to make a regular impact with Pep Clotet's side.
To date, he has made 17 appearances and scored one goal for Blues, which came in the 2-1 home win over Middlesbrough in October.
The former Spanish Under-19 international's last start came in the 3-0 loss away to Hull City in December
The Andalusia club are currently second in the table, three points off the top, and pushing for promotion to LaLiga.