Hezbollah did not specify how many different bodies the parts came from
Israel's military says human remains handed over by Hezbollah were of five Israeli soldiers killed in the 2006 war with the Lebanese Shia movement.
Military sources said four had died when their helicopter was shot down two days before the conflict ended.
The fifth was killed by an anti-tank missile in a separate incident.
The remains were delivered on Sunday after Israel released a Lebanese-born man who had served six years in prison for spying for Hezbollah.
Correspondents say the exchange raised speculation that there had been progress in indirect talks between Israel and Hezbollah over a broader prisoner swap.
This could involve two Israeli soldiers captured by Hezbollah in 2006 - an incident which prompted the 33-day war - and a number of Lebanese citizens held by Israel.
"The remains have been given to the families of the fallen soldiers from the summer 2006 war waged against Hezbollah and will be buried," an army spokesman said late on Monday.
Hezbollah handed over the box of body parts to the international Red Cross as Nissim Nasser was released, without specifying the numbers involved.
Mr Nasser was born in Lebanon to a Jewish mother and a Shia Muslim father. He left the country in 1982 and became an Israeli citizen.
Israeli media have said Hezbollah may have been holding the remains of 10 soldiers who died in the fighting.
There was no comment from Hezbollah about the apparent exchange, while Israel denied that the deportation of Nissim Nasser was part of any wider deal.