Samba seals switch to big-spending Anzhi
Samba, who joined Rovers in 2007 from Hertha Berlin, had been unhappy at Ewood Park for some time.
Last month he had a transfer request rejected by the Premier League strugglers and later criticised the club's Indian owners Venky's for "not understanding English football."
Big-spending Anzhi, bankrolled by billionaire Suleiman Kerimov, appointed Dutchman Guus Hiddink as coach earlier this month.
Anzhi have also signed big-name players such as Cameroon striker Samuel Eto'o and Brazilian defender Roberto Carlos in the last year.
The transfer window closed in Russia on Friday.