The 21-year-old had been on trial with the Scottish club following his release from Lyon earlier this summer.
Having done enough to impress manager Ally McCoist, the centre-back has now become the club's sixth signing in recent days.
"I am very happy to have signed for Rangers. It is a big club and I have good memories of the club in France," he told the club's official website.
"I was in the stadium on Saturday with 50,000 fans and that was beautiful.
"So for me it is very exciting to sign a contract here as a young player."
Faure will now go into the squad for Sunday's match against Berwick Rangers.