The defender has been playing his club ball in Europe since signing for PSV in May of 2008 and will be introduced by America on Thursday.
"We're losing an experienced player who collected merits for the VfB during the one-and-a-half years that he has been here," Stuttgart manager Fredi Bobic said in a statement.
Bobic says that Rodriquez dreams of being the Mexican national team's captain for the 2014 World Cup in Brazil and sees his best chance of attaining that goal coming by playing in Mexico.
"Maza came and asked us to release him. He wants to captain the Mexican national team at the 2014 World Cup in Brazil and to do that, he has to play regularly," Bobic said. "He feels that the opportunity to do that is the highest in his home country."