Amar, 42, was arrested and confessed to killing the soldier, whom he knew because they worked at the same restaurant in the coastal city of Bat Yam in central Israel, the agency said. The military identified the slain soldier as Sgt. Tomer Hazan, 20, of Bat Yam.
According to Shin Bet, the Palestinian recounted how he had picked up Hazan in a taxi on Friday after persuading him to accept a ride. He took the Israeli to an open field, killed him and hid his body in a well, the agency said.
Israeli forces raided Amar's home early Saturday, interrogating and arresting Amar and his brother.
Shin Bet said Amar confessed to intending to trade Hazan's body for another brother in an Israeli jail since 2003 for his role in several terror attacks. He then showed the Israeli forces where the body was hidden.
The agency did not say how Amar persuaded the soldier to join him on the ride Friday.
A senior military official said initial investigations suggested that Palestinian individuals planned the attack on their own, not on the orders of any militant groups. The official did not elaborate on who else may have been involved in the plot besides Amar. The jailed brother had been involved in shootings and bombings, the official said.
Hazan had a noncombat position in the air force and had an arrangement allowing him to hold a job outside the military at the restaurant, where he knew the Palestinian, the official said. He was killed with a "cold weapon" not a firearm but the official would not disclose the weapon used.
Such cases are rare, but it is not the first instance of Palestinians abducting Israeli soldiers, sometimes killing them afterward. The military has a longstanding campaign warning soldiers not to accept rides from strangers.
In 2001, a Palestinian woman lured an Israeli teenage boy over the Internet to the West Bank, where he was slain by waiting Palestinian militants.
The woman, Amna Muna, was released in 2011 along with more than a thousand other Palestinian prisoners in exchange for a single Israeli soldier, Gilad Schalit, held captive in Gaza by Hamas-allied militants. That deal was the most lopsided prisoner swap in Israel's history. The country was at the time torn between freeing Palestinians involved in bloody attacks like bus bombings and bringing a soldier home. It still touches a raw nerve in Israel.
Yitzhak Ilan, a former deputy head of the Shin Bet, told channel 10 TV that by finding Hazan's body quickly, a wider strategic incident was averted because it meant the remains couldn't be used as a bargaining chip, as in some past cases.
Ilan said Israel has thwarted dozens of abduction attempts by Palestinians in recent years.
Israel is holding about 5,000 Palestinian prisoners on charges ranging from rock throwing to deadly attacks. They are seen as heroes within Palestinian society.