Tractate Bava Batra 14b
"And who wrote the books of the Bible? Moses wrote his own book, i.e., the Torah, and the portion of Balaam in the Torah, and the book of Job. Joshua wrote his own book and eight verses in the Torah, which describe the death of Moses. Samuel wrote his own book, the book of Judges, and the book of Ruth. David wrote the book of Psalms by means of ten elders of previous generations, assembling a collection that included compositions of others along with his own. He included psalms authored by Adam the first man, by Melchizedek king of Salem, and by Abraham, and by Moses, and by Heman, and by Jeduthun, and by Asaph, and by the three sons of Korah."
KING DAVID (73)
3-9, 11-41, 51-65, 68-70, 86, 101, 103,
108-110, 122, 124, 131, 133, 138-145
ADAM (2)
92, 139
MALCHIZEDEK/SHEM (1)
110
AVRAHAM/ETHAN (1)
89
MOSHE (1)
90 (there are opinions that the following 10 psalms are also written by him)
YEDUTHUN (3)
Some scholars state that it is Adam.
Some others think that this term refers not to a person at all,
but decrees that were passed over him and over Israel....
39, 62, 77
SOLOMON (2)
72 - (some scholers attribute it to King David)
127 - (the ideas in this psalm similar to other books of King Solomon)
ASAPH (12)
50, 73-83
SONS OF KORACH (11)
42, 44-49, 84-85, 87-88
HEMAN coauthored Psalm 88)
EZRA (???)
ANONYMOUS (48)
Note: This is just one of the possible lists of authors. There are differences in interpretation by jewish scholars about some minor details.