'once' functions here as a conjunction, so its meaning is 'as soon as'. All of the examples you have cited are correct; it depends on what you want to covey.
In the present tense:
once it completes (
something that runs on its own, say, a programme) or is completed (
by somebody), I will submit the documents.
Here the emphasis lies in the current condition, the completed state. You may be describing a routine, a fact, or the process in general.
In the present perfect:
Once it has been completed, I will submit the documents.
Here you hint at the process that started some time in the past and is ongoing, and then you describe what you want to do after that. In this case, you are more likely to describe the particular process that you are now dealing with or has just dealt with. There is a retroactive element to this version.
But for general purpose and intent, the essential meaning is the same.