Prime Minister Haider al-Abadi claimed the city was liberated but the US-led coalition that has been helping Baghdad from the air said there was "still work to be done".
Celebrations began when the black jihadist flag was replaced by Iraq's tricolour on the main provincial headquarters in central Tikrit yesterday following a big military push.
Yet the fate of hundreds of IS fighters thought to have been holed up in former president Saddam Hussein's hometown for a bloody last stand was unclear today.
A spokesperson for the 60-nation US-led coalition that has carried out air strikes against IS in Tikrit and across Iraq suggested it was premature to claim victory in the month-old battle.
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"Parts of the city remain under (IS) control and there is still work to be done," Major Kim Michelsen told AFP by email.
US President Barack Obama's deputy envoy for the coalition, Brett McGurk, said Iraqi forces had made "encouraging progress" in Tikrit.
"Snipers are still there and many buildings are booby-trapped," Karim al-Nuri told AFP in the northern Tikrit neighbourhood of Qadisiya.
In scenes captured in an AFP video yesterday, jubilant fighters could be seen tearing up the black flag amid extensive destruction in the city.
"We are in the centre of Tikrit. The city and all administrative buildings were completely liberated," said one of them, policeman Bahaa Abdullah Nasif.
There was no immediate information on how many fighters were killed, wounded or captured in the fighting.