The commission was set up in 1999 to verify that Iraq no longer possessed weapons of mass destruction and had complied with obligations not to acquire proscribed armaments.
Inspectors from Unmovic left Iraq in March 2003, just before the US-led invasion started, and have never returned.
Iraq Survey Group
The Iraq Survey Group (ISG), a US-led coalition organisation, was tasked with continuing the hunt for WMDs in Iraq, but none were found.
The failure to discover suspicious weapons in Iraq undermined the main US and British argument for invading Iraq.
The closure of Unmovic comes after two years of US calls for an end to all related UN inspection work there.
Demetrius Perricos, the acting executive chairman of the group, told the council that the resolution "closes a cycle of many years of verification, where the UN showed that it can implement successfully the activities demanded by the international community, despite difficulties and frequently a lack of co-operation from the inspected party."
Shortly before the Unmovic vote, Perricos warned that fighters in Iraq may try to acquire poisonous agents for use in weapons.
"In the present security environment of Iraq, the possibility should not be discounted that non-state actors may seek to acquire toxic agents or their chemical precursors in small quantities," he said.
Perricos cited the example of the recent reported use of toxic industrial chemicals, such as chlorine, by fighters in Iraq.
"The possibility of non-state actors [insurgents] getting their hands on other, more toxic, agents is real," he said.