Israel as a kingdom is mentioned by the Egyptian Pharaoh Merneptah in an inscription in Egypt from 1200 BC. Therefore, we know that there was a kingdom called Israel at least that early. We also know from several inscriptions including the Tel Dan Stela that there was a King David who probably provided a bunch of uniting impetus enough to have a dynasty named after him who lived around 1000 BC. By the later Iron Age, the Divided Kingdom was fairly prominent, with King Jehu being depicted as offering tribute to a king of Assyria in the Black Obelisk of Shalmaneser III. King Ahab of Israel fought several wars against the Arameans (ancient Syria-Damascus) and even the Hittites, and there are some inscriptions (the Kurkh monoliths) which mention Ahab's large force of chariots and soldiers that he brought to the battle of Qarqar. In addition, the area was prominent enough for the Assyrians to make the sack of Lachish (an important Judahite city) into a massive sculptural relief which depicts the attack.

Therefore archaeological and textual records confirm the existence of a Israel and Judah as kingdoms during the Iron Age.

If you want more detailed information on the tons of other records and archaeological studies that concern the ancient Israelites, please check out Grabbe, Lester L. Ancient Israel: What Do We Know and How Do We Know It?London: T & T Clark, 2007, which you can preview on Google Books. It's the best overview of all the evidence that's out there, and is extremely well-researched and thorough.