About 50 soldiers from the army's rabbinical branch, using pickaxes in driving rain, disinterred the bodies from a cemetery in northern Israel, close to the town of Rosh Pina.
They were then placed in wooden caskets before being hoisted onto army vehicles.
A total of 59 bodies are due to be handed over on Thursday at the Lebanese-Israeli border crossing of Rosh-Hanikra through a Red Cross intermediary.
The army's northern regional commander, General Benny Gantz, arrived at the cemetery late in the morning to supervise the operation, with the area declared a closed military zone.
Under the terms of the German-brokered agreement, Israel will also release more than 400 Arab prisoners.
In exchange, Hizb Allah will turn over Elhanan Tannenbaum, an Israeli it claims is a spy whom it captured in October 2000, and the bodies of three soldiers, Adi Avitan, Benny Avraham and Umar Sawayid.
Among the prisoners set for release are Shaikh Abd al-Karim Ubaid and Mustafa Dirani, who were captured by Israel in 1989 and 1994, and held in exchange for news on missing Israeli pilot Ron Arad.
Quraya welcomes swap
Palestinian prime minister Ahmad Quraya gave his backing on Monday to the prisoner exchange which will also see hundreds of Palestinians go free.
"We view this accord between Hizb Allah and Israel favourably and we will not spare any effort to obtain the freedom of all our prisoners," Quraya told journalists in this West Bank town.
Ubaid(L) and Dirani (R) are among
the prisoners to be released
The Palestinian Authority on Sunday hailed the prisoner swap, but ministers complained the Authority had not been consulted and was still seeking the release of all "political prisoners."
About 7500 Palestinians are currently detained in Israeli jails, according to Palestinian prisoners' rights groups.