Yes, the bold phrase is quite common, but the correct pattern for the bold text is "on the something of something", so you need a definite article the in front of arrival. In addition, luggage is uncountable, so you should not put a in front of it.
I would also suggest that "the receiver of it" is not very elegant: better to say "the recipient".
You might also want to consider replacing keep with place or put, as placing the luggage in the store room is the only thing that happens immediately on the arrival of baggage. Keeping it in the storeroom is what happens for some time, after it has been placed there. The refined sentence would be:
On the arrival of luggage, place the luggage in the storeroom and notify the recipient.