The supreme court ruled last month that settlers were the lawful owners of the building in the heart of the occupied Palestinian city, ending a legal dispute lasting nearly seven years.
"Following the court decision... Defence Minister Moshe Yaalon today (Sunday) approved habitation of the house," his office said in a statement.
It added that the area military instructor had been told to allow "a limited number of families to the house".
The Peace Now settlement watchdog condemned what it called a "sad decision from the ministry of defence to approve and support the most radical rightwing settlers and approve them a new settlement in Hebron."
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The Rajabis, a Palestinian family, has for years said its four-storey building had been taken over fraudulently by Israeli settlers.
A lower court in 2012 accepted their claim, ruling that the settlers' assertion that they had legally purchased the property "does not hold water".
The supreme court overturned that judgement on appeal.
The building is near a contested holy site known to Muslims as the Ibrahimi Mosque and to Jews as the Cave of the Patriarchs in a tightly controlled Israeli enclave where many streets are off-limits to Palestinian cars.
The flashpoint city of Hebron, home to nearly 200,000 Palestinians, also comprises some 80 settler homes in the centre of town for about 700 Jews who live under Israeli army protection.