Zhirkov joined Chelsea in an £18million deal from CSKA Moscow in the summer of 2009 but struggled to hold down a first-team berth, partly due to injury problems, and leaves with a year remaining on his contract.
The 27-year-old, who passed a medical on Saturday morning, was presented to his new club's fans prior to Anzhi's 2-0 win over Tomsk in the Russian Premier Liga in the afternoon. A statement on fc-anji.ru read: "FC Anzhi has come to an agreement with Chelsea for transfer of the of Russian national team player Yury Zhirkov to our club."
It continued "This morning the newcomer to our team, after a medical check-up, signed a four-year contract."
Speaking to the club's fans ahead of Saturday's game, Zhirkov said: "I am very glad to be here in Makhachkala. I did not expect such reception. It is fantastic.
"I want to thank Anji fans and wish to our team great success."
Zhirkov, who according to reports in Russia has cost ambitious Anzhi around £13million, leaves Stamford Bridge after making 48 first-team appearances.
Source: PA
Source: PA