Ehud Olmert, the Israeli prime minister, acknowledged for the the first time on Sunday, that the Israeli soldiers to be returned as part of the deal were dead.
Olmert was quoted as telling his cabinet on Sunday: "Our initial theory was that the soldiers were alive ... Now we know with certainty there is no chance that that is the case."
The prime minister said that the exchange was "a matter of the highest moral order".
"Despite all hesitations, after weighing the pros and the cons, I support the agreement."
David Chater, Al Jazeera's correspondent in Israel: "The crucial thing in this [cabinet vote] was the decision of the Israeli prime minister himself to put his weight behind the idea of prisoner exhange."
While the deal will see the two soldiers returned, Israeli authorities have dropped a longstanding demand that the fate of Ron Arad, the Israeli airforce navigator who disappeared two decades ago, form part of the deal.
"His body has not been brought from the battle field and that's a very controversial subject," said Chater.
Indirect negotiations between Israel and Hezbollah have been handled by a UN-appointed German mediator.
Samir Qantar is the highest-profile Lebanese prisoner that would be released, who is currently serving multiple life terms for an attack on an Israeli town in 1979.
In addition to Qantar, Israel is also supposed to release four other Lebanese prisoners and the bodies of around 10 Hezbollah fighters.
Hezbollah had demanded the release of hundreds of Palestinian prisoners, but Israel said it was only willing to release between five and 10, a senior Israeli government official said on Sunday.
In parallel to the Hezbollah talks, Olmert's government is trying, via Egypt, to recover Gilad Shalit, a soldier captured by Hamas in Gaza around the same period.
Olmert in 2006 ruled out any negotiations for the captured soldiers, launching a military offensive in Gaza and a 34-day war in Lebanon. More than 1,200 Lebanese, mostly civilians, died in the conflict, as well as 157 Israelis.
The heads of Irael's Shin Beth internal security agency and of its Mossad foreign intelligence sevice are said to have urged ministers to vote against the deal.