The capital club have taken advantage of the summer sale in Dagestan by signing the three Russia internationals for undisclosed fees, all to be unveiled on Friday
The capital outfit did not disclose any details, either in terms of the size of the transfer fees or the length of the contracts involved, but vice president Gennady Solovyov did confirm that the Russia trio would be presented to the media on Friday.
"You will be able to see Kokorin, Denisov and Zhirkov at the Dinamo training ground as early as [Friday]," Solovyov told Izvestia. "The new players will be presented there."
Although midfielder Oleg Shatov's move to Zenit was announced on Wednesday, Denisov, Zhirkov and Kokorin are the first high-profile players to leave Anzhi following the announcement by club owner Suleiman Kerimov of the implementation of immediate and severe cost-cutting measures.
The billionaire had pumped €200 million (£170.7m) into his hometown club since taking charge in January 2011 but is now overseeing one of the biggest fire-sales in football history.
Indeed, speculation remains rife that football's highest-paid player, three-time Champions League winner Samuel Eto'o, and Brazil international Willian will also be sold before the close of the transfer market.