Experienced Swedish international Olof Mellberg has signed a one-year contract at relegated Spanish outfit Villareal.
Zapata has signed for Serie A giants AC Milan on a season-long loan, while Rodriguez has also moved to Italy to join Fiorentina.
A statement on Villareal's official website said: "Olof Mellberg has successfully completed his medical at the Jaime I de Castellon, and has signed a contract with the club for the next season.
"The defender will train with the team tomorrow, following which he will be presented to the press at the Ermita de la Mare de Deu de Gracia."
Mellberg has 116 caps for Sweden and was at the heart of his country's defence during this summer's European Championships in Poland and Ukraine.