"The nine will be delivered to the Iraqi side at 2.30pm (1130 GMT) today," Mohammed al-Waili, the governor, said.
Waili said on Tuesday that the Iraqi coast guards had boarded an Iranian-skippered ship suspected of smuggling oil in Iraqi waters when they were overpowered by an Iranian patrol.
Iran initially denied the incident, but then its envoy to Baghdad on Wednesday accused the Iraqi vessels of having encroached on Iranian waters.
The envoy said Tehran was investigating Iraq's claims that the coast guard patrol had been detained.
The affair is a test of the new warmth in relations between Baghdad and Tehran since pro-Iranian Shias took control in Iraq after US forces overthrew Saddam Hussein in 2003.
Iraq and Iran have a long history of disputes along the waterway. Iran briefly seized three British naval patrol boats in the same area in June 2004, at a time when US-led forces were responsible for policing the border.