The 28-year-old left-back, who made his Russia debut under Fabio Capello against Israel in a World Cup qualifier in September, becomes the first major signing for the wealthy club from the volatile North Caucasus region in the off-season.
Anzhi, coached by former Russia boss Guus Hiddink, have assembled an expensive, including Cameroon striker Samuel Eto'o and Brazil's 2002 World Cup winner Roberto Carlos.
"I hope working under such master as Guus Hiddink and along side such great players as Samuel Eto'o and Roberto Carlos would help my development," Yeshchenko was quoted as saying by Anzhi's website.
Anzhi, who went into a winter break in second place trailing league leaders CSKA Moscow by two points, face Bundesliga's Hannover in the Europa League last 32 tie next month.
The Russian season resumes in mid-March.