The 27-year-old joins from Benfica after a three-year stint at the Estadio da Luz in which he won the Primeira Liga, the Taca de Portugal and the Taca da Liga.
His performances in Lisbon helped gain the attention of some of Europe's premier clubs, with Manchester City and Bayern Munich reportedly also keen on acquiring the former Real Madrid man.
However, he will move to the four-time Russian champions after the FIFA World Cup and will remain under contract until 2019.
With his exit confirmed, Garay paid tribute to Benfica's president Luis Filipe Vieira and coach Jorge Jesus.
"I want to thank everyone who supported me in these three magnificent years I spent at Benfica," he told the Portuguese club's official website.
"In particular the president, who believed and invested in me and the coach who helped me evolve and reach a level of which I am very proud.
"Of course, I also thank all my colleagues with whom I had the honor to play at this club."
Garay will link up with former Porto coach Andre Villa-Boas in Russia as well as compatriot Cristian Ansaldi.
