Old Testament Canonisation

The Torah is canonised by Moses.
Then Moses wrote this law and gave it to the priests, the sons of Levi, who carried the ark of the covenant of the LORD, and to all the elders of Israel. (Deuteronomy 31:9 ESV)

It was recognized as scripture by his successors.
And there, in the presence of the people of Israel, he wrote on the stones a copy of the law of Moses, which he had written. (Joshua 8:32 ESV)

And Hilkiah the high priest said to Shaphan the secretary, “I have found the Book of the Law in the house of the LORD.” And Hilkiah gave the book to Shaphan, and he read it. (2 Kings 22:8 ESV)

Some process of canonisation may have occurred before the final canonisation of the entire Old Testament by Ezra.

David might have canonised some psalms.
This collection of the prayers of David son of Jesse ends here. (Psalm 72:20 NET)

Some canonisation of Old Testament may have occurred during the reign of Hezekiah by "the men of Hezekiah".
These also are proverbs of Solomon which the men of Hezekiah king of Judah copied. (Proverbs 25:1 ESV)

There is a "the book of the LORD" in the time of Isaiah, but the contents of this book are not identified.
Seek and read from the book of the LORD: Not one of these shall be missing; none shall be without her mate. For the mouth of the LORD has commanded, and his Spirit has gathered them. (Isaiah 34:16 ESV)

Jeremiah quote from Micah.
And certain of the elders of the land arose and spoke to all the assembled people, saying, "Micah of Moresheth prophesied in the days of Hezekiah king of Judah, and said to all the people of Judah: 'Thus says the LORD of hosts, "'Zion shall be plowed as a field; Jerusalem shall become a heap of ruins, and the mountain of the house a wooded height.' Did Hezekiah king of Judah and all Judah put him to death? Did he not fear the LORD and entreat the favor of the LORD, and did not the LORD relent of the disaster that he had pronounced against them? But we are about to bring great disaster upon ourselves." (Jeremiah 26:17-19 ESV)

Daniel also understood from some books about the word of the LORD to Jeremiah the prophet.
In the first year of Darius the son of Ahasuerus, by descent a Mede, who was made king over the realm of the Chaldeans - in the first year of his reign, I, Daniel, perceived in the books the number of years that, according to the word of the LORD to Jeremiah the prophet, must pass before the end of the desolations of Jerusalem, namely, seventy years. (Daniel 9:1-2 ESV)

Zechariah quoted from some former prophets.
Should you not have obeyed the words that the LORD cried out through the former prophets when Jerusalem was peacefully inhabited and her surrounding cities, the Negev, and the Shephelah were also populated? (Zechariah 7:7 NET)

"Do not be like your ancestors, to whom the former prophets called out, saying, 'The Lord who rules over all says, "Turn now from your evil wickedness,"' but they would by no means obey me," says the Lord. "As for your ancestors, where are they? And did the prophets live forever? But have my words and statutes, which I commanded my servants the prophets, not outlived your fathers? Then they paid attention and confessed, 'The Lord who rules over all has indeed done what he said he would do to us, because of our sinful ways.'" (Zechariah 1:4-6 NET)

The Old Testament refers to many non-Biblical sources, but they are not part of the scriptures:
The Book of the Wars of the Lord (Numbers 21:14)
The Book of Jasher (Joshua 10:13; 2 Samuel 1:18)
The Book of the Acts of Solomon (1 Kings 11:14)
The book of Nathan the Prophet (1 Chronicles 29:29)
The Book of Gad the Seer (1 Chronicles 29:29
The Prophecy of Ahijah the Shiloite (2 Chronicles 9:29
The Visions of Iddo the Seer (2 Chronicles 9:29)
The Book of Shemiah the Prophet (2 Chronicles 12:15)
The Book of Jehu the Son of Hanani (2 Chronicles 20:34)
The Sayings of Hosai (2 Chronicles 33:19)