Kuchuk was reappointed on Monday as a replacement for Viktor Goncharenko, who parted company with the club last Thursday.
The 55-year-old Belarusian was previously in charge at Kuban for the second half of the 2012-13 campaign, guiding them to fifth place in the top flight and UEFA Europa League qualification.
Following that successful spell, Kuchuk switched to Lokomotiv Moscow but was removed from his post in September with the capital club languishing in ninth in the table after finishing third last term.
Along with the poor performances on the field, a breakdown in relationship between Kuchuk and his players was one of the reason for his sacking, which has prompted a turnaround in fortunes for a Lokomotiv team that is unbeaten in their last seven games in all competitions.
Kuchuk will hope to redeem himself in his second stint with Kuban, who are in fifth spot after the first 13 games of this season and are level on 24 points with city rivals Krasnodar and Terek Grozny.
However, he faces a substantial task if he is to claim all three points in his first game at the helm on Saturday against a Zenit team that will be looking to bounce back from a 3-1 home loss to Terek last time out.
