So person A is talking to person B.
A is saying he will move, B asks when, and A responds "tomorrow", and after that he adds the following sentence:
ここに来るようになったぐらいだったかな、決まったの。
I guess it roughly means "It has been decided around the time since I started coming here."
I want to know what the ように means in this case.
ように means:
in order to / so that / hoping or wishing for something
However I can't really fit in these meanings with this sentence.
As you have correctly guessed, dictionary-form + ようになる means "(gradually) come to ～", "learn to ～", "start to ～", etc. You can find many examples on JGram and on ALC. よう (様 in kanji) is a word which has many meanings including style/manner, status, way/method or appearance. ～ようになる may be interpreted as something like "become a status of doing ～", but it's better to memorize this pattern as-is.
The sentence says "As I recall, it was when I started to come here that it was decided."
