The 37-year-old former Real Madrid defender was targeted by fans during violent protests against the team following their shock early exit from the Libertadores Cup last week.
"We gave him all our assurances (for his safety) here at Corinthians. He has his own motives," Andres Sanches, president of the Brazilian club, said.
"He's a guy of 38 already, he received a good offer from abroad and by mutual accord we decided to free him," Sanches told reporters.
Brazilian media said Roberto Carlos would be joining Anzhi Makhachkala in Russia in a 5.0 million euros one-year deal.
They also said he had been made an offer by Los Angeles Galaxy but for less.
Roberto Carlos, who was nursing a thigh injury, did not play in Corinthians' 2-0 defeat away to Deportes Tolima of Colombia 10 days ago in the second leg of their Libertadores Cup preliminary tie.
They went out 2-0 on aggregate having been held 0-0 at home in Sao Paulo in the first leg.
Since then he and captain Ronaldo, his team mate when Brazil won the 2002 World Cup in Asia, have been the main targets of fans' ire over Corinthians' failure to progress in South America's Champions League equivalent which they have never won.
VIOLENT PROTESTS
In one of the most violent protests, the team coach with players on board was attacked by stone-throwing fans as it arrived at the club's training grounds.
"Corinthians will be under pressure every day but none of our players was hit... some things overstepped the limit a bit and that of course makes things very difficult not only for the players but also the club," Sanches said.
Roberto Carlos joined Corinthians at the beginning of 2010, the club's centenary year, with a view to helping them win the Libertadores Cup but the team were eliminated by fellow Brazilian side Flamengo in the round of 16.
Despite that, he had a good season and was voted the best left back of the Brazilian championship. He played 64 matches and scored five goals.
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