The final scene gives the clearest clue
The book ends long after Jerusalem has fallen. Babylon's army has burned the temple, broken down Jerusalem's walls, and carried many people away from Judah (2 Kings 25:8-12). Those events place the closing chapters in the period of exile.
Then comes one more dated event. Jehoiachin, the former king of Judah, is released from prison by Evilmerodach, king of Babylon, and receives regular provision at the Babylonian court (2 Kings 25:27-30). Since the writer includes this news, 2 Kings must have been completed after it happened. Scripture does not tell us exactly how long afterwards.
And it came to pass in the seven and thirtieth year of the captivity of Jehoiachin king of Judah, in the twelfth month, on the seven and twentieth day of the month, that Evil–merodach king of Babylon in the year that he began to reign did lift up the head of Jehoiachin king of Judah out of prison;
It looks back from exile
2 Kings is more than a timeline of kings and battles. It explains why two kingdoms that God had established came to an end. The northern kingdom of Israel was taken by Assyria after its people persisted in idolatry and refused to listen to God's warnings (2 Kings 17:6-8).
Judah saw Israel's downfall, yet eventually faced Babylon's conquest as well (2 Kings 24:14-16). From the shadow of exile, the writer helps God's people face the truth about their history. Their loss was not proof that the Lord had forgotten them. It showed the seriousness of ignoring his covenant.
For so it was, that the children of Israel had sinned against the Lord their God, which had brought them up out of the land of Egypt, from under the hand of Pharaoh king of Egypt, and had feared other gods,
The writer drew on earlier records
The author did not begin with an empty page. Throughout 2 Kings, the book points to records called the chronicles of the kings of Israel or Judah for further details about particular reigns (2 Kings 1:18; 2 Kings 23:28). That suggests the writer used earlier royal records while shaping a faithful account of Israel's story.
Some Jewish and Christian traditions connect 2 Kings with Jeremiah because he lived through Judah's final years. But the book itself does not name its author. So the most careful answer is simple: an unnamed writer or editor completed 2 Kings after Jehoiachin's release, using older sources and writing with the exile clearly in view.
A dark ending with a small light
The date matters because it helps us hear the book as exiled people may have heard it. They had lost their land, their city, and their temple. Yet the final image is not only one of judgement. Jehoiachin is brought out of prison, honoured, and given an ongoing place at the king's table (2 Kings 25:28-30).
That does not erase Judah's pain or excuse its sin. Still, it leaves a quiet sign of hope. God had judged his people, but the line of David and God's purposes had not disappeared. As you read 2 Kings, watch for both its honest warnings and these small reminders that God is still at work.
And he spake kindly to him, and set his throne above the throne of the kings that were with him in Babylon;