Although there are small groups of Iraqi soldiers still fighting back, most have apparently escaped the town.
The Kurdish forces are now pushing into another city, Mosul.
But not everyone is happy with the Kurds' success in Kirkuk.
Turkey - the country directly to the north of Iraq - says it is unacceptable that the Kurds are allowed to control the city.
They are worried that Kurdish people might try and build their own brand new country in the north of Iraq - something the Turkish government really doesn't want.
New day in Baghdad
In Baghdad, Iraqis have been waking up to a very different city a day after dramatic and historical scenes.