Iraqi Prime Minister Haider al-Abadi earlier announced that pro-government forces had retaken the second city from IS after a months-long battle that killed thousands of civilians and forced nearly a million people from their homes.
"The recovery of Mosul from the hands of (IS) marks a decisive step in the campaign to eliminate terrorist control in parts of Iraq and to free its people," the EU foreign affairs chief Federica Mogherini and its aid commissioner Christos Stylianides said in a joint statement yesterday.
"It is now essential that a process of return and the re-establishment of trust between communities begins, and that all Iraqis are able to start building a shared future," they said.
IS still controls swathes of western Iraq including much of the desert Anbar province and rival forces, which largely cooperated against the jihadists in Mosul, are expected to compete for a share of the spoils.
Abadi himself has faced accusations of incompetence and corruption in his government, and followers of popular cleric Moqtada Sadr have staged large protests in Baghdad calling for electoral reform.