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.

up vote 5 down vote accepted

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."

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