The 30-year-old, who left Loftus Road at the end of last season, has agreed a one-year deal with the Russian outfit, with the option of a 12-month extension.
He made 29 appearances for QPR, scoring 10 goals.
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."
Kuban will play in the third preliminary round of the Europa League after finishing fifth in the Russian Premier League last season.