Anzhi announced on their official website that the 37-year-old, who lifted the World Cup with Brazil in 2002, had agreed to a two-and-a-half year deal to move back across the Atlantic.
Carlos had requested a move away from his home nation after receiving relentless abuse and harassment for missing Corinthians' Copa Libertadores elimination.
He is expected to receive around €5 million a year to appear in the team which narrowly avoided relegation from Russia's top division last year, but affirmed that the move was not financially motivated.
"I am going to Russia extremely intrigued. When I decided to continue my career in in this country, money was not a crucial factor," the player had told Sport-Express as negotiations were being finalised.
Carlos will make his debut at the end of this month against Zenit St Petersburg in the Russian Cup.
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