The 29-year-old joins the German side for an undisclosed fee and has signed a three-year deal that will keep him at the Mercedes Benz Arena until the summer of 2014.
Stuttgart general manager Fredi Bobic told the club’s official website: “After losing Mathieu Delpierre to injury we were out to sign one more player in that position.
“Maza is fully aware of the standards of the game in Europe and will therefore not require any warm-up time.”
Rodriguez added: “Personally the transfer from PSV to Stuttgart is a new challange. Stuttgart is a big club with a high reputation inside and outside Germany.”