The Bible says God is always the one who establishes who the authorities are. So naturally it was God who sent Saul to the prophet Samuel to be anointed king of Israel. When Samuel privately anointed Saul, he said it was God’s doing. After that, Samuel publicly cast lots as a way of letting God choose a king. They brought out Saul after he was chosen by lot, and Samuel described him as “the man the Lord has chosen“.

But in a later speech to the people of Israel, Samuel described Saul as “the king you have chosen“. And later, God told Solomon he had never chosen anyone to be the ruler of Israel. So it definitely wasn’t God who chose Saul. It was the people.