Rabbi's Corner, Scripture Authors

One authoritative, ancient Jewish tradition about who wrote what in the Old Testament is preserved as follows...

Who wrote the Scriptures? — Moses wrote his own book and the portion of Balaam and Job. Joshua wrote the book which bears his name and [the last] eight verses of the Pentateuch. Samuel wrote the book which bears his name and the Book of Judges and Ruth. David wrote the Book of Psalms, including in it the work of the elders, namely, Adam, Melchizedek, Abraham, Moses, Heman, Yeduthun, Asaph, and the three sons of Korah. Jeremiah wrote the book which bears his name, the Book of Kings, and Lamentations. Hezekiah and his colleagues wrote (Mnemonic YMSHK) Isaiah, Proverbs, the Song of Songs and Ecclesiastes. The Men of the Great Assembly wrote (Mnemonic KNDG) Ezekiel, the Twelve Minor Prophets, Daniel and the Scroll of Esther. Ezra wrote the book that bears his name and the genealogies of the Book of Chronicles up to his own time.
--Soncino Babylonian Talmud: Seder Nezikin: Tractate Baba Bathra: 14b-15a

The tractate continues discussing parts and pieces that different authors contributed, clarifying, for instance, who wrote of Moses' death [Joshua], who wrote of Samuel's death [Gad the Seer], which psalms were written by Adam, Melchizedek, or Abraham, etc. There is even a record of several rabbis thinking Job was post-exilic:

R. Johanan and R. Eleazar both stated that Job was among those who returned from the [Babylonian] Exile, and that his house of study was in Tiberias.
--Ibid, 15a