Votes are still being counted, with a big victory for "yes" expected.
Kurds say it will give them a mandate to negotiate secession, but Iraq's PM denounced it as "unconstitutional".
The referendum passed off peacefully across the three provinces that make up the region, and turnout was estimated at about 72%, according to the electoral commission.
There were scenes of celebration as the polls closed in the regional capital, Irbil, and in the disputed city of Kirkuk, where a curfew was imposed on Monday night amid fears of unrest.