The 34-year-old midfielder, whose Zenit St Petersburg contract ended last month, scored 17 goals in 74 internationals.
He played most of his career at Zenit before moving to English side Arsenal in 2009, where he netted 23 times in 105 games. He rejoined Zenit in June 2013, after a short loan spell back at the club the previous season.
Kuban, who are based in the south and finished 10th last term, appointed a new coach in June when Dmitri Khokhlov, who once played with Arshavin for Russia, took over.
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OUR VIEW
Andrei Arshavin had the look of a world beater when he took Euro 2008 by storm. He made an excellent start to his Arsenal career before it tapered off quite sharply. By the time he left Arsenal he appeared shorn of confidence. He may not have hit previous highs following his return to Zenit but Arshavin remains a lavishly talented footballer who, at 34, still has plenty to offer.
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