Prime Minister Ehud Olmert urged the cabinet to approve the deal even though the two soldiers, Eldad Regev and Ehud Goldwasser, were dead.
"Our initial theory was that the soldiers were alive ... Now we know with certainty there is no chance that that is the case," he said. "We have no illusions: there will be much sadness in Israel, much humiliation considering the celebrations that will be held on the other side."
Hezbollah, which is regarded as as a terrorist group by Israel, proclaimed it had succeeded in "dictating the terms" of the swap.
Regev and Goldwasser were captured by Hezbollah guerrillas in a deadly cross-border raid on July 12, 2006 that sparked a devastating 34-day war in Lebanon.
Israeli ministers said it could take about two weeks for the swap to be carried out.
"In exchange for the return of the abducted soldiers, the state of Israel will release prisoners and detainees being held in its prison facilities, and will transfer bodies and information," the government said in a document approved by the cabinet.
"Prisoner Samir Kantar and four illegal Lebanese fighters being held by Israel will be released to Lebanon," it said.
Kantar, a member of the Palestine Liberation Front, is serving a life term after being sentenced in 1980 to 542 years in prison for killing two men and a four-year-old girl in a 1979 attack that shocked Israel.
Israel will also hand over the bodies "of dozens of infiltrators and terrorists, including eight members of Hezbollah," the document said.
Once the deal is carried out, Israel will release Palestinian prisoners.
"The number and identities of the prisoners will be determined at the sole discretion of the state of Israel," it said.
Hezbollah executive council chief Hashem Safie Eddin said the agreement was a victory for the Shiite group.
"The world could not achieve the Israeli goal of recovering its soldiers without the resistance dictating its terms: the release of prisoners," he said during a ceremony in southern Lebanon.
Olmert said Hezbollah's goal from the very beginning had been to secure Kantar's release through its seizure of the soldiers, a move which triggered a war that left 1,200 people, mostly civilians, killed in Lebanon and 160 people, most of them soldiers, in Israel.
The heads of the Shin Beth internal security agency and the Mossad foreign intelligence agency had urged ministers to vote against the deal.
But Olmert's spokesman Mark Regev said Israel had "a moral obligation" to bring back its servicemen.
"In these negotiations we have been forced to deal with Hezbollah, a cynical terrorist organisation that has no qualms about manipulating the pain of our servicemen families."
Deputy Prime Minister Haim Ramon said the proposed exchange had been held up for about a year because Hezbollah leader Hassan Nasrallah initially demanded the release of thousands of prisoners.
"It was only when he left the number and identity of the Palestinian prisoners up to Israel that the deal went through," Ramon told army radio.
On June 1, Israel freed and deported to Lebanon a convicted Hezbollah spy and the Shiite militant group handed over the remains of Israeli soldiers killed in 2006.
Last October, Israel handed over a Hezbollah prisoner and the remains of two militants in return for the body of an Israeli and information on the fate of airman Ron Arad, missing since 1986.
In January 2006, Nasrallah said the airman was probably dead although he had no proof.
The largest prisoner swap between the two sides took place in January 2004 when Israel released 400 Palestinians and 31 others, including 23 Lebanese, in exchange for an Israeli reservist and the remains of three Israeli soldiers.
