The 29-year-old has made just two Premier League appearances under Martin Jol this season, with Sascha Riether - on loan from Koln - and Aaron Hughes preferred at right-back.
McDermott revealed earlier on Friday that he was close to securing his second signing of the window - following the arrival of former Sporting Lisbon captain Daniel Carrico.
The move signals another new defender for the relegation-threatened side, who have conceded the second-highest amount of goals in England's top flight this season with 40 in just 21 games.
Reading find themselves in 19th place in the Premier League, level on 13 points with bottom club QPR, five points from safety.