Probably not the answer you want to hear but... It really does depend on the person, as well as other factors such as if you already know a second language. As the other comment mentions, its been documented to take 88 weeks or so, but I'd take this with a grain of salt. I've seen people study Japanese for only a year and reach a surprising level of competency, whilst others have studied 4+ years and are next to hopeless. It really does depend on how much time and effort you are willing to put in.
My advice, though, would be to not get too caught up on the whole "fluency" thing. Too many people get fixated with it and end up disappointed or depressed when they don't reach a certain level within a given time. Just have fun with the learning process and enjoy meeting new people (and, of course, work hard). If you do that, I think the "fluency" side of things will naturally take care of itself.
Good luck!