Nicolas Anelka has announced on his Twitter account that he is to leave West Brom with immediate effect.
Mauricio Pochettino expects to be at Southampton next season and is looking forward to working with chairman Ralph Krueger.
The France Under-20 international has signed a three-year deal at the Stadium of Light and becomes the seventh man to join the club since the end of last season.
He has already joined up with his new team-mates and manager Paolo Di Canio at their training camp in Italy.
A product of Le Havre's youth set-up, Ba broke into the first team set-up at the beginning of 2012 and went on to make 12 league appearances.
He follows Valentin Roberge, Modibo Diakite, Cabral, Jozy Altidore, David Moberg Karlsson and Duncan Watmore into the club, and the list of newcomers could be boosted further within the next 24 hours.