The order, confirmed by two people familiar with the matter, applies to outposts established by settlers without official authorisation from the Israeli state.
Outposts typically consist of prefabricated caravans and house a small number of settlers.
Israel has from time to time demolished such structures and also formally recognised others, allowing them to access government funding.
It was not immediately clear when the operation would begin.
Separately, Israel's Supreme Court ruled on Sunday that Israeli defence authorities must enable the safe return of three Palestinian families to their homes, after they were chased out by settlers, in the West Bank village of Jalud.
UN bodies and most governments deem all Israeli settlements illegal under international law and consider the West Bank to be occupied territory under military control. Israel argues the territory is disputed, not occupied.
Netanyahu had ordered the eviction of the unauthorised outposts in response to pressure from the United States, the country's closest ally, the sources said.
US Ambassador to Israel Mike Huckabee on Saturday denounced violent settlers as terrorists and called for them to face severe consequences following a meeting with several Palestinian Americans in a West Bank Palestinian town.
Israeli website Ynet earlier reported the orders targeted around 100 outposts across the occupied territory.
The Israeli prime minister's office and the military, who would normally take part in clearing any outposts in the West Bank, did not immediately respond to a request to comment.
Finance Minister Bezalel Smotrich, asked at a conference in Jerusalem about the Ynet report, said Netanyahu has given "an instruction to evict places built in Areas A and B", referring to parts of the West Bank in which most Palestinians live.
Under the Oslo Accords, interim peace agreements reached in the 1990s between Israel and the Palestine Liberation Organization, the West Bank was split into three zones: A, B and C.
Smotrich, a settler himself who has overseen settlement housing projects and formally recognised homes built illegally, said while he disagreed with Netanyahu's decision, the government had made huge strides in advancing settlements in Area C.
There are 340 outposts in the West Bank along with 146 settlements formally recognised by the Israeli government, according to Peace Now, an Israeli organisation that is critical of settlement expansion and advocates for a two-state solution.
Last month, Israeli settlers besieged the homes of Palestinians in a nearby village, including one owned by a Palestinian American, before the military forced them from the area. The village's Palestinian residents have said they have continued to face harassment and intimidation by Israeli settlers.
