Miguel Herrera has been fired as Mexico coach following allegations that he punched a television reporter.
Former Arsenal midfielder Abou Diaby has rejected an offer to join West Brom in favour of finding a new club in France.
The 22-year old has signed a three-and-a-half-year deal at the Stadium of Light after completing his medical and agreeing personal terms.
N'Diaye, a France Under-21 international who started his career at Ligue 1 side Nancy, becomes Sunderland's first signing in the January transfer window.
Black Cats boss Martin O'Neill told his club's website: "Alfred is a strong, powerful young player and as such can offer us more strength in depth.
"He will give us options and I'm delighted that we have been able to bring him to the club."
The defensive midfielder, who can also play at centre-back, arrived at the club's training ground on Tuesday to discuss a move to Wearside from the Turkish Super Lig club.
N'Diaye signed for Bursaspor from Nancy last year for a fee reported to be 3 million euros (£2.5 million) and could be available for this Saturday's Premier League match against West Ham at the Stadium of Light, subject to international clearance.