The soldier was later named as Dvir Sorek from the West Bank settlement of Ofra. He was not in uniform at the time of the attack.
Security forces launched a large-scale manhunt for his killer after his body was discovered. The army was working on the growing assumption that the soldier had first been abducted and that he had not been murdered at the site where his body was found.
Troops conducting searches of the area on Thursday morning entered the West Bank town of Beit Fajjar, close to where Dvir's body was found.
The Islamic Jihad terrorist organization welcomed the murder, calling it "heroic and sending an important message."
The IDF has launched an extensive investigation together with the Shin Bet and the police, working on the assumption that attack was carried out by an as-yet unidentified terror cell.
Sorek had been missing since Wednesday evening.
"In the early morning, a soldier's body was found bearing stab marks near a settlement in the (Gush Etzion) area," the IDF said.
"The soldier was on a (joint) track of yeshiva studies (and military service)," the army said. "The IDF, the Shin Bet security service and the police are on the scene and searching the area."
Prime Minister Benjamin Netanyahu issued a statement saying that security forces were "in pursuit now in order to capture the despicable terrorist and bring him to account."
IDF Spokesman Brig. Gen. Ronen Menalis said: "During the night, we received a report of an 18-year-old boy whose relatives had been unable to contact him since late evening.
"They reported this to us very late at night. We gathered forces from the Etzion Regional Division, including trackers," he said.
"During the night, around 2.30-3am, soldiers found the young man's body near the entrance to Migdal Oz (and) his death was pronounced. He had been stabbed and killed," Menalis said.
"We understand that this was a terror attack. The slain youth is a resident of Binyamin and a yeshiva student in Migdal Oz. He had begun his recruitment into the IDF but had not yet served. He was still in the studying stage at the yeshiva. He is from a well-known family in the Judea and Samaria," he said.
Gush Etzion Regional Council head Shlomo Ne'eman said in response: "Gush Etzion awoke to a difficult morning of innocent blood being spilled by despicable murderers. We are a steadfast settlement, having endured bereavement and heroism. We will not weaken as a nation or as an enterprise.
"Our bitter enemies will repeatedly try to hurt us, but our response is the response of the Gush Etzion fighters in the War of Independence, to be ever more determined," he said.
"We send our condolences to the dear family who are in pain, and to the settlement where the hero studied," Ne'eman said. "And to the Israeli government we say again – bring this war to an end in victory."
Rabbi Shlomo Vilk, head of the yeshiva at which Sorek studied, told Ynet that the 19-year-old had been out buying gifts for his teachers when he disappeared Wednesday evening.
"He was found with the books that he had bought for his rabbis," Vilk said.
"He chose not to buy religious books, but the most recent novel by David Grossman, which he was clutching when he was discovered. One of our challenges is to be careful not to translate this murder into feelings of hatred, fear and isolation. We cannot let them drag us down and become like our enemy."