The author is not named
Unlike several New Testament letters, 1 Kings doesn't begin by telling readers who wrote it. The book's author remains unnamed, and Scripture does not identify Jeremiah, Ezra, or any other individual as its writer.
That means the most honest answer is simple: we don't know for certain. Jewish tradition has often named Jeremiah, perhaps because the book speaks with the same deep concern for covenant faithfulness and the consequences of idolatry found in Jeremiah's ministry. But tradition is not the same as a statement made by the book itself.
This needn't weaken its message. The Bible presents 1 Kings as part of Israel's Scripture, and its focus is far more on God's faithfulness than on the identity of the human writer.
The writer used earlier records
The author was not making up a story from memory. While recounting Solomon's reign, he refers readers to a record called the book of the acts of Solomon (1 Kings 11:41). Later he points to chronicles concerning the kings of Israel and Judah (1 Kings 14:19; 1 Kings 14:29).
Those works have not been preserved as part of the Bible. Still, their mention shows that the writer drew on royal records and shaped this material into a theological history. He didn't merely ask what happened at court. He asked whether each king listened to the Lord.
And the rest of the acts of Solomon, and all that he did, and his wisdom, are they not written in the book of the acts of Solomon?
Why 1 Kings was written
1 Kings begins with Solomon's wisdom, the building of the temple, and a united kingdom. Yet it also shows Solomon turning towards other gods, then the nation dividing under Rehoboam and Jeroboam. Again and again, the story measures rulers by their response to God's commands, not by wealth, military strength, or popularity.
At the temple dedication, Solomon calls the people to give God their whole heart (1 Kings 8:61). That concern runs through the entire book. Even dramatic figures such as Elijah are not presented as heroes for their own sake. Their ministry exposes Israel's divided loyalty and calls the nation back to the Lord.
Let your heart therefore be perfect with the Lord our God, to walk in his statutes, and to keep his commandments, as at this day.
Read 1 Kings as a witness to God
The books of Kings continue beyond 1 Kings and eventually describe Judah's exile. The closing chapter of 2 Kings records Jehoiachin's release from prison in Babylon, showing that the final form of this history was written or completed after those events (2 Kings 25:27-30). That still does not tell us the writer's name.
So, was Jeremiah the author? It is possible according to longstanding tradition, but it cannot be proved from Scripture. What can be seen clearly is the writer's purpose: God speaks, warns, keeps his promises, and patiently calls his people back. As you read, watch for that thread in the lives of Solomon, Jeroboam, Ahab, Elijah, and the ordinary people living under their rule.