It is the first time that archae-ologists have found a monumental building thought to be associated with him. This discovery, together with other finds from the site, is likely to transform the academic world's understanding of early Israelite history.
The building, about 30 metres square, is thought to have contained up to 50 rooms on two, or possibly three, floors, arranged around a central courtyard.
The excavation of the building, carried out this month and last month, has revealed that the occupants of the palace area had a liking for exotic stone and ceramic tableware, and other goods manufactured as far away as Egypt and Cyprus.
The archaeologists have found fragments of Egyptian alabaster bowls, and Cypriot perfume vessels, as well as locally produced pottery jars, and evidence of metal-working.
The palace was found inside the remains of an ancient city that has been excavated by archaeologists over the past seven years.
The discoveries are important because they seem to confirm an important element of the biblical account of Israelite history: that state formation and urbanism began in the Jerusalem area in about 1000 BC - that is, in the period traditionally associated with King David.
Over recent decades, many archaeologists have tended to dismiss the idea that the Davidic and Solomonic period really represented the establishment of a substantial centralised state in the Jerusalem area. Some have believed instead that state formation in that area - later culturally central to Judaism, Christianity, and Islam - did not begin until about 300 years later.
The new discoveries, however, suggest that they were wrong, and that King David may indeed have presided over the creation of a powerful and centrally organised proto-Jewish state.
This year's excavation also unearthed the remains of another building thought to date from David's time - a royal warehouse for storing tax-in-kind. The site, at Khirbet Qeiyafa, 20 miles south-west of Jerusalem, is thought to be that of the biblical city of Shaarayim.
In the account in the Bible, the area is famous for being the place where the young David killed the Philistine "giant" Goliath, with a stone.
At that period, the Iron Age, the Philistines, and the early Kingdom of Judah (of which David became king) were vying with each other for local political and military dominance.
Indeed, Shaarayim seems only to have existed for 20 to 30 years before it was destroyed, almost certainly by the Philistines.
The archaeologists have found the destruction level, with collapsed buildings in which pots, stone vessels, and even metal artefacts were still sitting on the floors where their owners had abandoned them.
The archaeologists believe that the city was not burnt by the attackers, but that all the buildings had collapsed when they were stripped of valuable timber roof-beams.
The archaeological investigation shows that Philistine fury was directed particularly fiercely against Israelite religious structures. Altars, ritual cleansing basins, and small models (symbolising the concept of a temple) had been deliberately smashed.
The excavations have been directed by Professor Yossi Garfinkel, of the Hebrew University of Jerusalem, and Saar Ganor, of the Israel Antiquities Authority.