The 34-year-old full-back spent last season with Napoli in Italy's Serie A, making 18 appearances before being released at the end of his contract.
Reveillere, who began his career at French club Rennes, was a member of the France squad at both the 2010 World Cup and Euro 2012.
He could make his debut against Arsenal on Saturday.

5 August 2016 Last updated at 13:26 BST
The fire at Regent Superbowl and indoor market in Great Yarmouth town centre started in the early hours.
Footage shows firefighters using aerial ladders and hoses to dampen down the building, which has been completely gutted by flames.

The deadline to enter the tournament, which begins on 24 November, was 28 October, but the 39-year-old five-time world champion has declined to enter.
He has not played in a competitive match since losing 13-9 to Stuart Bingham in the quarter-finals of the World Championship in April.
O'Sullivan beat Judd Trump 10-9 in last year's final to win his fifth UK title.
This month, O'Sullivan also announced he would not be defending his title at the Champion of Champions event in Coventry, which begins on 10 November.
The UK Championship is broadcast live by the BBC and is one of snooker's 'Triple Crown' events, along with the Masters and the World Championship.
O'Sullivan's withdrawal will disappoint many fans of the popular competition, which is staged at the Barbican Centre.
A spokesman from World Snooker, the sport's governing body, said they were still expecting "a great event" and that ticket sales were "extremely good".

The discussion centred mainly on the gas market, energy security and the risks of having to rely on supplies from Russia in the distant future.
But, actually, the report says, the short-term risks in the gas market of things such as having to pay more for imports and security of supply are minimal.
The £500m is actually made up of technical factors involving the electricity market, specifically if the UK fails to negotiate continued membership of the Internal Energy Market (IEM).
That cost comes from things such as losing access to more efficient cross-border energy trading systems.
But the report is clear such costs could be avoided if the UK remained part of the IEM, as non-EU members such as Norway have managed.
The report is also concerned about the possibility of it becoming more expensive to finance big investment projects such as new power stations, but that is not part of the £500m.
And it mentions potential problems involving the UK finding "itself excluded from EU 'solidarity principles' in which European nations agree to supply to their neighbours in the event of a gas supply crisis".
It stresses the uncertainty surrounding the forecasts, but concludes: "The impact of Brexit on the UK energy system is very likely to be negative."
But it does not say at least £500m, it says up to £500m.
Reality Check verdict: There is considerable uncertainty about the figure and much of the effect could be avoided by staying in the IEM.
READ MORE: The facts behind claims in the EU debate
Sunderland have signed former France international Anthony Reveillere on a deal until the end of the season.
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Aerial pictures show the scale of the blaze that broke out at a Norfolk seaside resort.
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Ronnie O'Sullivan will not be defending his UK Snooker Championship title in York in November.
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A Vivid Economics report prepared for the National Grid shows leaving the European Union would put an extra £500m a year on to UK energy bills, Energy Secretary Amber Rudd has told BBC Radio 4's Today programme.