Killing Duri -- who was vice president at the time of the 2003 US-led invasion and has for years been the most senior member of Saddam's regime still at large -- would be a major victory for Baghdad.
Ketaeb Hezbollah says the man killed by pro-government forces on Friday was Duri, but he had previously been reported dead only to resurface in audio and video messages.
"Today, we handed over the body of the criminal Izzat al-Duri to the Iraqi government" after confirming his identity with "tests and also testimony from those who previously met him", Ketaeb Hezbollah spokesman Jaafar al-Husseini told journalists.
Ketaeb Hezbollah -- one of the most powerful militias fighting alongside government forces against the Islamic State (IS) jihadist group -- delivered the body in a heavily armed convoy of dozens of vehicles to a blocked-off section of street in central Baghdad.
It was transferred in a transparent container to a white Mercedes van, which then departed.
A health ministry official, speaking on condition of anonymity, confirmed it had received the body and would conduct DNA testing.