According to Holy Orthodox Tradition, King David wrote the Psalms. Higher Criticism ridicules this fact. But Jewish oral and written tradition confirms and affirms Orthodox traditional beliefs, the Psalms are the prayers of King David indeed. Admittedly, the mechanism for the transmission of these prayers is complicated and fascinating.
Listen to what the Jewish community has to say,
"Who Wrote the Book of Psalms?
From Chabad.org
Question:
I was always under the impression that King David was the author of the book of Psalms (Tehillim). But as I read through the psalms, I saw that many of them are attributed to other composers: Moses, Asaph, Heiman, and others. What’s the deal?
Answer:
A quick perusal through the Book of Psalms will reveal numerous chapters attributed to various great personalities.
The Talmud enumerates ten authors other than King David. “David composed the Book of Psalms through ten elders: Adam, Melchizedek, Abraham (1. See Notes), Moses, Heiman, Yedutun, Asaph, and the three sons of Korach.”(2) Furthermore, according to the Midrash, Jacob recited psalms during his 20-year stay in Laban’s home.(3)
Clearly, many psalms were composed and recited many generations before King David, yet Psalms is popularly known as the book of King David! The Talmud states that Rabbi Meir would say, “All the praises stated in the book of Psalms were recited by David, as it is stated: ‘The prayers of David, son of Yishai, are ended (kalu).’(4) Do not read kalu; rather, read kolelu, - ‘all of these’”—which indicates that the entire book of Psalms consists of the prayers of King David.(5)
To clarify this conundrum, we must first properly appreciate the unique stature of Psalms. It is the only book in Tanach that is compared to the Torah itself.(6)
More than just a collection of beautiful songs composed by various authors, it is considered the “Bible of Prayer.” Just as all of Torah is sourced in the five books of Moses, prayer in Judaism is sourced in the five books of Psalms. For all generations, Psalms gives every Jew, be he a great sage or a simpleton, the ability to best express and articulate supplication and thanksgiving to his Creator.(7)
Why, of all the great leaders of history, did G‑d ordain King David, the “Sweet Singer of Israel,” (8) to be the one to redact the songs of praise from the beginning of time, and to bequeath to the Jewish nation the gift of prayer?(9)
Because during his entire life, King David was immersed in the constant recitation of psalms. In times of trouble and success, as a hunted fugitive(10) and as the victorious king at the pinnacle of royalty and greatness,(11) his lips never ceased to sing the praises of G‑d.
Although many psalms were originally composed by others, it was King David’s recital that established them as immortal songs of praise.
FOOTNOTES
1. Psalms 89. Eitan HaEzrachi refers to Abraham (see Talmud, Bava Batra 15a).
2. Talmud, Bava Batra 14b.
3. Bereishit Rabbah 68:12.
4. Psalms 72:20.
5. Talmud, Pesachim 117a.
6. Midrash Tehillim; foreword to Psalms by Rabbeinu Yosef ibn Yahya.
7. See Maamarei Admor Hazaken 5565, vol. 1, page 56.
8. II Samuel 23:1.
9. Yalkut Shimoni, Tehillim 613: “May the words of my mouth be acceptable” (Psalms 19:15): King David prayed that his words should be inscribed for posterity.
10. Psalms 52 and 54.
11. See Talmud, Berachot 4a."