"Today Anzhi signed Lassana Diarra and (Russian striker) Nikita Burmistrov. Their transfer underlines our ambition to fight for the most prestigious trophies," Anzhi director Aivaz Kaziakhmedov told the club's website.
Anzhi did not give any details about the length of Diarra's contract or the transfer fee.
The Russian summer transfer window closes on September 10.
The defensive midfielder joined Real from Portsmouth in 2008 but failed to become a regular starter with the Spanish giants.
Diarra, 27, joins a host of well-known internationals at the big-spending club from the volatile North Caucasus region, including Cameroon striker Samuel Eto'o.
Anzhi, bankrolled by billionaire Suleiman Kerimov and coached by former Russia boss Guus Hiddink, have reached the group stage of the Europa League after winning all six of their qualifying matches and scoring 15 goals while conceding none.