Is it "He was appointed manager of the office" or "He was appointed as the manager of the office"?
That one's a little tricky. Instead of "manager," I'll use "President." Standing alone that is a title of an office, a status, a position, or whatever you might want to call it. Whoever holds it is "the President."
Trump was elected President. (not "the" president, although you might say elected to the office of President, or elected to be President). On the other hand, you would say:
Trump is the President.
So, in your case, I would say (if asked) that he is "the manager" because he was appointed to that position.
From the example I gave, "appointed manager" would be preferred to appointed as the manager, althouigh I personally wouldn't use either phrasing.