The 67-year-old, who has coached Anzhi on three separate occasions earlier in his career, takes over from the former Manchester United assistant coach amid turbulent times at the Russian club.
The news comes after club president Konstantin Remcukov took to his Twitter page to hint that the likes of Samuel Eto'o, Willian, Igor Denisov and Aleksandr Kokorin could all be sold as he looks to bring some financial stability to the club.
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The club's budget reached £116 million in 2011 and with billionaire owner Suleiman Kerimov, Russia's 19th richest man, losing £242m in shares in fertiliser giant Uralkali on July 30, changes are set to be made.
Defeat to FC Rostov in the Russian Premier League last week, which leaves Anzhi in 13th place, saw Kerimov tell Sport Ekspress that the club was "not worth wasting nerves and health on".
However, the big-spending Russians have since released the following statement on their website regarding the situation, suggesting that any changes will not be wholesale.
"There is no discussion of any kind of mass selling-off of the football players or of any other measures discussed in the media. The club will respect all of the contractual obligations of its players.
"The team will be founded on long-term perspectives for the development of the club, which of course assumes certain changes in its team makeup."
The statement also added that the budget changes made necessary by Uefa's Financial Fair Play regulations "will not contribute to any essential degradation of the team".