Rabbinic tradition says that some of the books in the Torah were written by Moises, I think Ecclesiastes is among those but my recollection of it is quite poor. I think the tradition should also name without too much issue the books about the exile from Babylon, since it's quite modern in the rabbinic timeline as far as the Old Testament goes.
Who actually wrote them? Nameless ascetic men, probably the few rabbis that actually had notions of written language and decided to compile tales that were mostly expressed by oral tradition. Between those speeches there were likely engravings in wood or a variety of visual cues that guided storytellers through the process. Translating and rewriting was an unforgiving task so they were likely minor figures from their respective eras.
The rest of the Bible was also recollected by relatively unknown names, but at least we have pseudonyms for a few of them. Paul did write his letters and he was a roman citizen that lived and had decent education, the letters for the other apostles are not so clear in that regard, a couple of them might be legit and others made afterwards from previous documents or later transmissions. Each text from the New Testament is attached to a particular figure so the assumed author is implied.
I'm no expert in the Quran, but it's much more recent and the Middle East was pretty enlightened at the time (much more so than Europe at that point), so their historical accounts on the book should be rather reliable. One way or another, the Prophet must've written at least a part of it although tradition has it that the text is an aspect of Allah, so technically it always existed.