West Brom have sacked Nicolas Anelka citing "gross misconduct" after the striker claimed on Twitter he had quit the club.
Mauricio Pochettino expects to be at Southampton next season and is looking forward to working with chairman Ralph Krueger.
The 32-year-old was released from his deal with Russian side Kuban Krasnodar and the Corsican club announced he would officially sign pending the successful completion of a medical on New Year's Day.
Cisse began his professional career with Auxerre before moving to Liverpool in 2004. He joined Marseille on loan in 2006 before making a permanent move to the Stade Velodrome the following year.
Since then he has changed clubs at regular intervals, having played for Panathinaikos, Lazio, QPR and Kuban plus Sunderland and Qatari side Al Gharafa on loan since 2008.
Cisse was first capped at senior level by France in May 2002 and played in that summer's unsuccessful World Cup campaign.
He missed the 2006 tournament after suffering a broken leg in a warm-up match but returned to the squad for the 2010 finals in South Africa.