The 27-year-old player submitted a transfer request in January and hasn't played for Rovers since their 2-1 defeat by Stoke at the start of last month. Samba was allowed to finalize the deal because the Russian transfer window didn't close until 8:00 PM GMT on Friday.
"I see it [the move] as a new challenge," Samba told Sky Sports News. "It's a small club that wants to become a very big one in Russia. A very powerful owner wants to transform the club and bring the club to greatness."
Samba has joined the growing list of star players signed by the club since billionaire Suleyman Kerimov became the owner in January 2011. Since then, they have named Guus Hiddink as manager and acquired players such as Brazil World Cup 2002 winner Roberto Carlos, Chelsea full-back Yuri Zhirkov, and Inter Milan striker Samuel Eto'o.
The France-born center-back joined Rovers in 2007 from Hertha Berlin and made 184 appearances for the Premier League team in all competitions, scoring 18 goals. He will wear the number 22 shirt at Anzhi.
Speaking at a press conference on Friday, Rovers assistant manager Eric Black backed his players to cope without Samba. He said: "He hasn't played for a few weeks and our performances have been exceptional. Obviously there was a blip at Arsenal, but again, you look at the performances against Newcastle, Fulham, and QPR and the guys who have been in there have done exceptionally well."
Blackburn travels to Manchester City on Saturday to play the Premier League leaders and is currently sitting one place outside the relegation zone in 17th place in the table.
Anzhi is based in Russia’s Dagestan republic, which borders Georgia and Azerbaijan. They were founded in 1991 but enjoyed little success until the arrival of Kerimov. Due to security problems in Makhachkala, the team lives and trains in Moscow and travels nearly 1,250 miles for home matches.
Anzhi is currently in seventh place in the Russian Premier League. Samba’s first league fixture could be on March 5 against Dynamo Moscow when the season resumes after the winter break.