The much-delayed reopening was brought forward in what officials said was a response to the destruction of priceless artefacts by Islamic State group jihadists in the northern city of Mosul.
"We have been preparing to reopen for the past couple of months, the museum should be open to everyone," Deputy Tourism and Antiquities Minister Qais Hussein Rashid said.
"The events in Mosul led us to speed up our work and we wanted to open it today as a response to what the gangs of Daesh did," he said, using an Arabic acronym for the IS group.
Militants are also seen defacing a colossal Assyrian winged bull in an archaeological park in Mosul with a jackhammer.
The destruction sparked global outrage, calls for an emergency meeting of the UN Security Council and fears over the fate of other major heritage sites in areas under IS control.
The Mosul destruction was the worst disaster to strike Iraq's treasure since the national museum in Baghdad was looted in the chaos that followed the US-led toppling of Saddam Hussein.