The France international has agreed a one-year contract with the Russian outfit, with the option to extend his deal by a further 12 months.
|CISSE LEAVES QPR
|5/1||QPR are 5/1 with William Hill to win the Championship next season
Kuban sporting director Sergey Doronchenko told the club's official website: "Cisse is not only a big name for FC Kuban, but he has ambitions this season.
"He wants to get back into the French national side with FC Kuban."
The 31-year-old will bring a wealth of experience after previous spells at the likes of Liverpool, Marseille and Lazio.
He joins a club that will play in the third preliminary round of the Europa League after achieving a fifth-place finish in the league last season.