The 21-year-old, younger brother of Chelsea and Belgium forward Eden, has spent the past two seasons on loan at Zulte Waregem in his homeland.
Thorgan was named as a standby player for the 2014 World Cup squad, having made one appearance for the senior team, and is yet to feature for the Stamford Bridge club since joining from French club Racing Lens in 2012.
Gladbach finished sixth in the Bundesliga last season.
(Reporting by Josh Reich, editing by Tony Jimenez)
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