Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
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.