The 24-year-old had his contract with Sevilla terminated last weekend, with the Spanish club confirming he was moving to Cardiff.
Cala has trained with his new team-mates throughout the week and is available for selection in Saturday's south Wales derby against Swansea.
A Cardiff statement said: "Cardiff City Football Club can confirm that Spanish defender Juan Torres Ruiz Cala has officially joined the club on a two-and-a-half-year deal."
Cala is Ole Gunnar Solskjaer's seventh signing following the arrivals of Magnus Wolff Eikrem, Mats Moller Daehli, Jo Inge Berget, Fabio, Kenwyne Jones and Wilfried Zaha.
Source : PA
Source: PA