The bodies of Naftali Frenkel and Gilad Shaar, both 16, and 19-year-old Eyal Yifrach were found near the village of Halhul in the West Bank close to the place where they were last seen alive earlier this month.
Israel has accused Hamas of abducting the youths as they were hitchhiking home, a claim the Palestinian militant group has repeatedly denied.
Their disappearance on June 12 triggered a massive Israeli search operation in Palestinian towns and cities.
In a statement, Mr Cameron said he was deeply saddened by what had happened to the teenagers, whose bodies were found yesterday.
"This was an appalling and inexcusable act of terror perpetrated against young teenagers," he said. "Britain will stand with Israel as it seeks to bring to justice those responsible. Tonight my thoughts and prayers are with the families of Gilad, Naftali and Eyal. No parent should have ever to suffer such heartache or grief."
Labour leader Ed Miliband said: "The murder of Naftali Frenkel, Gilad Shaar and Eyal Yifrach is awful news. This was an utterly reprehensible act of terrorism."
An Israeli army spokesman said the bodies were going through forensic identification and the families of the abducted teenagers had been notified.
Shin Bet said the bodies had been buried in a field near the village of Halhul, just north of Hebron.
Binyamin Proper, who was among the civilian volunteers who found the bodies, said a member of the search party "saw something suspicious on the ground, plants that looked out of place, moved them and moved some rocks and then found the bodies". He added: "We realised it was them and we called the army."
The discovery ended Israel's largest ground operation in the Palestinian territory in nearly a decade which had raised fears of renewed fighting with Hamas.
Israel's prime minister said the Hamas militant group will pay a heavy price for the deaths of the teenagers.
Benjamin Netanyahu said in a statement: "Hamas is responsible, and Hamas will pay." He added the teenagers "were kidnapped and murdered in cold blood by wild beasts".
Mr Netanyahu was meeting with his Security Cabinet to discuss a response.
Palestinian President Mahmoud Abbas condemned the kidnappings, and his forces worked closely with Israel during the search.
But Mr Netanyahu has called on Mr Abbas to dissolve a unity government recently formed with the backing of Hamas, saying it is impossible to be committed to peace while sitting with a group that kidnaps Israelis.
In Washington, White House spokesman Josh Earnest said: "We obviously condemn in the strongest possible terms violence that takes the lives of innocent civilians."