I think the meaning is "He is right. I am also right." He, as well as I, is right.
We are taught that when you have an "as well as" phrase, you make the verb agree with the main subject. In this case, it's "he" so you're right using "is."
However, the ear rebels at hearing "I is" next to each other, so my best advice is to ignore the fact that you are grammatically in the clear and restate it: He and I are both right. He and I -- we are both right.
(I dont know why "I are" doesn't sound as grating as "I is" but it doesn't.)