Basic meanings: reach the point where ~; come to ~; come to be that ~; have finally become
Comments: Some change takes place gradually
jakuson-san wa nihongo ga hanaseru you ni natta.
Mr. Jackson has reached the point where he can speak Japanese.
hayasi-san wa sake o nomanai you ni natta.
Mr. Hayashi doesn't drink [alcohol] anymore. (lit. Mr. Hayashi has reached the point where he no longer drinks [alcohol].)
tui ni, muzukasii nihongo ga yomeru you ni natta.
Finally, I've reached the point where I can read difficult Japanese.
mou sugu wakaru you ni naru yo.
You'll soon come to understand.
nakada-san wa watasi to hanasanai you ni natta.
Miss Nakada doesn't talk to me anymore.
kanji ga yomeru you ni naranakatta.
I haven't yet reached the point where I can read kanji.
kitanaku suru hito ga takusan ita node, ima wa kono kyousitu de tabemono o tabete wa ikenai you ni natte iru.
Because there were so many messy people, we're no longer allowed to eat food in this classroom.
- Although ように (you ni) indicates a gradual change, it can have the meaning of a sudden change when an appropriate adjective (such as 急に [kyuuni] = suddenly) is used. However, ~なくなる (-naku naru) is more typically used to express non-gradual change.
- ようになっている (you ni natte iru) indicates the state resulting from change that has come about after a (usually long) process. Generally, the state is considered to be permanent or at least not likely to change in the forseeable future. For instance, you could could use ようになっている to describe a street that has become so badly damaged that you can't drive on it any more, or a road that's closed for the time being, or something like in example sentence 5.
- Note the differing meanings of the two ways of negating the expression, as in key sentence 2 and example 3 (negating the associated clause), and example sentence 4 (negating なる [naru]).