"Yuri Krasnozhan is our new coach. Today he will be officially presented to the team," Krasnodar governor and Kuban president Alexander Tkachyov wrote on his Twitter account.
Krasnozhan, 49, replaces Romanian Petrescu who left suddenly on Tuesday saying he needed a "new challenge."
Media reports said 44-year-old Petrescu is set to take over the country's oldest football club Dynamo Moscow, bottom of the league.
Sergei Silkin resigned as Dynamo coach last week after they lost their first four games having failed to score a goal and conceding nine.
He was sacked by Lokomotiv a few months later despite them being among the league leaders at the time.
The club said he was fired for "negligence in his job" following a controversial defeat by Anzhi Makhachkala.
In December, Krasnozhan was appointed coach of Anzhi but this time he lasted only five weeks before being sacked by the wealthy club from the volatile North Caucasus region.