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.
Ba, 20, broke into Le Havre's first-team set-up at the beginning of 2012 after coming through their academy ranks and went on to make 12 league appearances for the French outfit in Ligue 1.
He follows Valentin Roberge, Modibo Diakite, Cabral, Jozy Altidore, David Moberg Karlsson and Duncan Watmore into the Wearside club.
Argentine side Velez Sarsfield, meanwhile, have confirmed they have agreed a deal with the Black Cats for full-back Gino Peruzzi and expect the transfer to be completed before the weekend.
Sunderland missed out on highly-rated Le Havre teenager Benjamin Mendy, a former team-mate of Ba's, when he opted to join Marseille instead, but look to have landed Peruzzi after the deal stalled initially over personal terms.
Reports from Italy also claim Di Canio is close to striking a deal for Juventus midfielder Emanuele Giaccherini, with around £8.6m required to release him from his contract in Turin.