Reveillere, who is thirty-four years old, was released in the summer by Italian giants Napoli and has been training at the Academy of Light with Gus Poyet's men in the hope of securing himself a contract.
With options in defence light, Gus Poyet has signed the defender to provide cover and competition for the likes of Billy Jones and Santiago Vergini, both of whom have played at right back at some point this season already.
Anthony will wear the number fifteen shirt - previously occupied by David Vaughan - and, pending clearance from the Italian FA, he should be available for the game at the Stadium of Light this weekend.
Last week Gus Poyet had this to say about the player:
"He played a lot in Italy last season and always played plenty of games in France. That shows you he’s a fit lad.
The problem in England is it’s completely different. You cannot compare it. People think we exaggerate that, but it’s true. Ask Ricky (Alvarez, on loan from Inter Milan). The first half-hour against Spurs, it was like he was on another planet. You need to see that and put it into games, which is the most difficult part. You can run, do whatever you like, but when you’re on the pitch, you realise how different English football is.
It would be nice to have a proper right-back replacement, or even left-back because he can play there."
Reveillere has enjoyed a relatively successful career, playing mainly in his homeland of France. He started out at Stade Rennes, before moving on to Lyon where he played in the Champions League and won five French league titles. He later moved on to the Italians Napoli, winning the Coppa Italia last season.
He's also played for France on twenty occasions, though has mainly found himself behind the likes of Lillian Thuram and Bacary Sagna in the pecking order. He was selected for the squads that traveled to the 2010 World Cup in South Africa and the European Championships in 2012, playing in the quarter final defeat to eventual winners Spain in the latter.
He's on Twitter - if you want to give him a follow, you can find him at @Reveillere_Off.
Oh - and we can't forget the obligatory Youtube video.