The defender joins Villarreal as a free agent after coming off contract at Las Palmas.
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Cardona has signed a deal to 2027 after making the move on Thursday.
He arrives as fellow left-back Alberto Moreno departs Villarreal for Como this week.
Cardona came through the system at Gimnàstic de Tarragona before leaving for Las Palmas, where he made his senior debut.