The second is correct. You could also say 'it has been successfully completed already' or 'it has already been successfully completed'. To me, that last variant sounds the most natural.

Well, if memory serves me well, we put adverbs 'already' before the main verb, which is 'been'. So, the second sentence is correct. Edit: on the second thought, both sentences are correct, but the second one is more common. I hope this helps.

First one ☝[emoji]