The 34-year-old full-back arrives on a free transfer, having been unable to find a club since his contract at Napoli expired at the end of 2013-14.
Before moving to Naples, Reveillere spent 10 years at Lyon, where he won five Ligue 1 titles, as well as the Coupe de France in 2008 and 2012.
Reveillere was part of the France squads for the World Cup in 2010 and the European Championship two years later, playing the full 90 minutes in his country's 2-0 defeat to Spain in the quarter-finals of the latter.
He could be in line to make his debut against Arsenal in the Premier League on Saturday, subject to international clearance from the Italian FA.
Sunderland head coach Gus Poyet bemoaned his lack of options in his backline this week and the Uruguayan will hope the signing of Reveillere will boost the defensive ranks after the 8-0 humiliation at the hands of Southampton last weekend.
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
