There are two answers, depending on how you look at it.
In human terms, Rehoboam and Jeroboam share the responsibility. Rehoboam was foolish, and Jeroboam was ambitious. Rehoboam became king of the 12 tribes of Israel when his father (Solomon) died in about 931BC. But he was quickly challenged by Jeroboam who became king of the northern ten tribes (which took the name Israel) and Rehoboam only retained control of Judah and Benjamin (which were jointly known as Judah). See 1 Kings 12 for the full story.
But it was really God’s doing, as 1 Kings 12:15 makes clear:
So the king [Rehoboam] did not listen to the people, for it was a turn of affairs brought about by the LORD that he might fulfill his word, which the LORD spoke by Ahijah the Shilonite to Jeroboam the son of Nebat.
That prophecy is found in 1 Kings 11:31-40. At the end of that prophecy, God told Jeroboam:
And if you will listen to all that I command you, and will walk in my ways, and do what is right in my eyes by keeping my statutes and my commandments, as David my servant did, I will be with you and will build you a sure house, as I built for David, and I will give Israel to you.
But alas, Jeroboam didn’t do that. Instead:
Jeroboam did not turn from his evil way, but made priests for the high places again from among all the people. Any who would, he ordained to be priests of the high places. And this thing became sin to the house of Jeroboam, so as to cut it off and to destroy it from the face of the earth. (1Kings 13:33-34)
And so the split become permanent.
There is, however, a prophecy that the two kingdoms would one day join again under one king (Ezekiel 37:15-22). That king will be Jesus.