The 21-year-old central defender has spent the past week on trial at Murray Park following his release from Lyon in the summer.
Faure was also on trial at Leeds United before arriving north of the border where has impressed Rangers boss Ally McCoist in training.
Faure, who is unable to play in Tuesday night's Ramsdens Cup tie at Falkirk, helped Les Bleus finish fourth in last year's FIFA Under-20 World Cup in Colombia.
Faure is McCoist's sixth summer signing, joining Dean Shiels, Kevin Kyle, Francisco Sandaza, Ian Black and Emilson Cribari at Ibrox.
He expressed admiration for the sell-out crowd in Saturday's 5-1 Irn-Bru Third Division victory over East Stirlingshire.
He told RangersTV: "I am very happy to have signed for Rangers. It is a big club and I have good memories of the club in France.
"The training was good, the players are good and the training centre is great.
"I was in the stadium on Saturday with 50,000 fans and that was beautiful. For me it is incredible because I knew Rangers from my time in France.
"So for me it is very exciting to sign a contract here as a young player."