The 37-year-old played at this summer's World Cup with Belgium, earning his 140th international cap in the 2-1 quarter-final loss to eventual champions Spain.
Witsel spent last season at Spanish club Girona, making 32 La Liga appearances, although he was unable to help the Catalan side avoid relegation.
His career has also included spells at Standard Liege, Benfica, Zenit Saint Petersburg, Tianjin Quanjian, Borussia Dortmund and Atletico Madrid.
Witsel has been recruited to help cover for Laurent Abergel, who suffered a serious knee injury during pre-season shortly after signing from Lorient.
He is expected to be available for Nice's Ligue 1 opener at home to Lorient on Saturday.