The 32-year-old Serbian had been linked with various clubs since it emerged that Chelsea would not object to him leaving during the January transfer window since a renewal of his contract beyond next season was not on the cards at Stamford Bridge.
Ivanovic has previous experience of the Russian league, as he played for Lokomotiv Moscow for two season prior to signing for Chelsea in 2008.
During his nine-year spell in West London, he helped the club win two Premier League titles as well as their sole Champions League crown, in 2012.