The 48-year-old replaces Andrei Gordeyev and Brazilian Roberto Carlos who took over in a joint caretaker capacity in September when the long-serving Gadzhi Gadzhiyev was sacked.
"The board of directors have appointed Yuri Krasnozhan as head coach of Anzhi Makhachkala," the wealthy club from the volatile North Caucasus region said on their website.
"The Russian coach has signed a five-year contract."
Krasnozhan was sacked by Lokomotiv in June despite the club being among the league leaders at the time. The railway side said he was fired for "negligence in his job" following a controversial defeat by Anzhi.
"I'm very grateful to the Anzhi bosses for entrusting me with these huge responsibilities," said Krasnozhan who made his name as a coach at North Caucasus rivals Spartak Nalchik.
POPULAR CLUB
"Anzhi have become one of the more popular clubs in recent times, followed not only in Russia but also round the world."
The club, bankrolled by billionaire Suleiman Kerimov, had been linked with several high-profile coaches including England's Fabio Capello, Real Madrid's Jose Mourinho and former Russia boss Guus Hiddink.
Russian Kerimov's money helped lure Cameroon striker Samuel Eto'o from Inter Milan during the last transfer window on a three-year deal.
According to media reports, Eto'o is now the highest-paid player in world football with an annual salary of 20 million euros.
Asked if he could deal with Eto'o and Roberto Carlos, who still plays at left-back, Krasnozhan said: "Anzhi are not just Roberto and Samuel. We also have a lot of other talented players, local guys.
"I don't have to control them. We must be as one, as a team."
Anzhi consultant German Tkachenko said he had been thinking of someone else for the job.
"We, as consultants, offered a different candidate for the head coaching post," Kerimov's close friend Tkachenko told Russian media. "But the club decided differently."
