Both sentences are intelligible to native speakers. However, more frequently used one is the former, '잘 도착했어요.'
도착했어요 itself is a verb. (past tense)
By adding 잘, which is an adverb, it modificates (add meanings to) the verb 도착했어요. So it literally means 'I arrived well.'
'도착 잘 했어요' literally means 'I performed arrival well' (It's weird to translate into English.) 도착 is a noun and its role in a sentence is an object. I won't go deep, but you need to make distinction between a part of speech and a role in a sentence.
In a nutshell, both are valid sentences. They're structurally different. '잘 도착했어요' is more frequently used.
I don't think there is an apparent reason why the former is more frequently used. It's a colloquial thing. Sometimes it's more useful to focus on 'what', rather than on 'why'.