It varies from person to person. I have seen a 13-year-old Dutch schoolboy with a very poor grasp of English become beautifully fluent after one term (three months) at an English boarding school. I have seen a 20-year-old Chinese dancer become perfectly fluent with an English accent after working for two years with a British ballet company. It depends on the person, his age and his language environment.

To my best knowledge, it takes 1000 hours of guided learning ('guided' means 'structured and controlled by a competent teacher') combined with at least 3000 hours of passive language exposure (reading/listening). My first language is Russian. I had spent about that amount of time before I was able to pass a CEFR C1 level exam. With a bit of exaggeration, I can be considered 'fluent' (I actually write ‘fluent in English’ in my CV), because I can speak fast and freely on almost any topic. Nevertheless, I still have a very noticeable accent and I make accidental grammar errors.