"It really is a dream come true for me. I have been a fan all my life, so to get the chance to play here is fantastic," Davis told the official Rangers website.
"Since the manager has been in charge, things have not worked out well for me so I welcome this chance to come to Glasgow.
"I'm finally getting my chance after missing out when I was a kid.
"Rangers are in a great position right now as they are challenging on all fronts and it will be fantastic to be a part of that."