The Palestinian man was arrested and confessed to the killing, the Shin Bet intelligence agency said.
The killing could deal a new blow to US-led Mideast peace efforts, which resumed in July after a nearly five-year break in Israel-Palestinian talks. The deaths of several Palestinians in Israeli arrest raids in the West Bank intended to detain militants involved in attacks have further soured the atmosphere between the two sides.
The search led the troops to Nidal Amar, a 42-year-old Palestinian from Beit Amin a village near the city of Qalqiliya in the northern West Bank.
Amar told the Shin Bet that he had killed the soldier, whom he knew because he worked together with him at a restaurant in the coastal city of Bat Yam in central Israel, the agency said.
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According to Shin Bet, the Palestinian recounted how he had picked up the soldier in a taxi yesterday after convincing him to accept a ride.
Israeli forces raided Amar's home early on today based on intelligence information, and interrogated Amar and his brother.
Shin Bet said Amar had confessed to intending to trade the soldier's body for another brother, in an Israeli jail since 2003 for his role in several terror attacks.
Amar showed the Israeli forces where the body was hidden today afternoon after his arrest.
It is not the first case of Palestinians abducting Israeli soldiers, sometimes killing them afterward. The military has a long standing campaign warning soldiers not to accept rides from strangers.