Wiktionary.com has two examples for ‘as well as’: conjunction and preposition.
Are the two sentences below grammatically correct?
(preposition) He as well as you is right.
(conjunction) He as well as you are right.
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The moon, as well as the stars, was shining down on them. is grammatically correct.
The commas are probably considered optional by some writers and grammarians, but they're helpful for indicating that as well as is a preposition here, so I'd say that they're necessary. M-W online shows this: ": in addition to : besides (the coach, as well as the team, is ready)". Merriam-Webster's Dictionary of English Usage recommends using the commas when the first subject is singular.
When as well as is used as a conjunction, it joins two elements without using commas, just as it would were the sentence The moon and the stars were shining down on them. M-W online shows this: ": and in addition : and (brave as well as loyal)".
Many native speakers make what are called "proximity errors". Many usage experts disagree on what "subject-verb agreement" means in sentences that have complex subjects with a singular and a plural element.
He as well as you are right is an example of a proximity error: "Under the 'proximity rule', the verb is governed by the element nearest to it."
See Merriam-Webster's Dictionary of English Usage pages 140-141, as well as, for a thorough discussion of the problem.
There is no definitive answer to your question.
The correct sentence is the following:
He, as well as you, is right.
The subject of the sentence is he for which you use is as verb, not are. "As well as you" is a parenthetical which doesn't change the subject of the sentence.
To use are, you should say something similar to the following:
He and you are right.
You are both right.