The 25-year-old passed a medical and signed a contract with an option for a permanent three-year deal which can be exercised before the end of June.
Faubert will be presented at the Bernabeu on Monday.
He is the Primera Liga side's third mid-season signing after they landed French midfielder Lassana Diarra and Dutch striker Klaas Jan Huntelaar.
Youth-team midfielder Dani Parejo has also been recalled from a loan spell and incorporated into the first team.
Faubert will help give coach Juande Ramos options on the right of midfield where they have lacked a natural wide player for the position.
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