But a senior Hamas official warned Israel against any reprisals, saying it would open "the gates of hell".
The discovery of the three bodies in a field in the southern West Bank came 17 days after the youngsters disappeared, triggering a huge manhunt during which five Palestinians were killed and more than 400 arrested.
It also triggered a surge in rocket attacks against southern Israel by militants in the Gaza Strip, which triggered retaliatory Israeli air strikes almost nightly.
But so far, the military has held back from attacking Hamas's power base in the Gaza Strip.
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"This evening, we found three bodies and all the signs indicate that they are the bodies of our three kidnapped youngsters," Prime Minister Benjamin Netanyahu told ministers at the start of an emergency session of his security cabinet.
"They were kidnapped and murdered in cold blood by human animals.. Satan has not yet invented vengeance for the blood of small child," he said.
The bodies were found in the southern West Bank near the town of Halhul, some 10 minutes from the roadside where they were last seen hitchhiking.
"During the search for Eyal Ifrach, Gilad Shaer and Naftali Frankel, the IDF discovered 3 bodies," the Israeli army said on Twitter.
Army spokesman Lieutenant Colonel Peter Lerner said the bodies had been discovered around 1400 GMT but he refused to comment on the cause of death.
"At around 5.00 pm, the IDF uncovered three bodies in the northwestern Hebron district," he told reporters, saying the bodies were being transferred for formal forensic identification.
One of the civilian volunteers involved in the search told army radio the bodies had been found under a pile of branches and stones in a remote area.
"Today, during a sweep with the army, one of the guys spotted something unusual, they started to move branches and stones and found the bodies," said volunteer Benny Truper.
"It was a very isolated area, more or less at the end of the world.