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State television said the governor's HQ had been recaptured and 60 fighters from the Isis militant group killed.
A spokesman for the rebels confirmed heavy fighting but implied the attack had failed, saying they were pursuing what was left of the army offensive.
The rebels control large swathes of the north and west after lightning raids that captured the second city, Mosul.
'Flee or be killed'
On Saturday, thousands of Iraqi troops backed by tanks and air power attacked Tikrit from four directions, state TV said.
It said there had been complete success in clearing Isis from the city, with some militant commanders among the 60 killed. It said the other insurgents there had fled.
Tikrit fell on 11 June to rebels of the Islamic State in Iraq and the Levant (Isis).
The BBC's Jim Muir, who is in northern Iraq, says that since then, the government has been threatening a counter-offensive from the next town down the Tigris river - Samarra - where the insurgents were finally checked.
State TV said preparations were now being made to move north towards Mosul.
The Iraqi soldiers are being supported in the offensive by allied Sunni tribesmen and Shia militias.
The attack on Tikrit included air strikes that targeted insurgents at a university campus to the north of the city.
Soldiers had captured part of the campus in a helicopter operation on Friday.
Army spokesman Lt-Gen Sabah Fatlawi had warned Isis fighters they "now have two choices - flee or be killed".
One Tikrit resident, Yousef, told the BBC there was still fighting in the city, in both northern and southern districts.
He said: "Most residents have already left Tikrit. Most have left for Kirkuk or Mosul. They are scared of being stuck in the middle of all the fighting. Only five families in my street have stayed."
Iraqi military sources said the offensive on Tikrit - the mainly Sunni hometown of former leader Saddam Hussein - was being co-ordinated with American military advisers.
However, although the US has confirmed it is flying armed drones in Iraq to protect US personnel on the ground, US officials say American troops are not directly involved in the hostilities.
Some 300 US military advisers have been deployed to Iraq.
Also on Saturday, fighting to the south of the capital Baghdad left at least 20 Iraqi troops dead. Police officials told AP dozens of insurgents were also killed.
Another army spokesman told Agence France-Presse that Iraqi forces were also now in control of a key road from Baghdad to Samarra.
Separately, Iraq's most influential Shia cleric called for a prime minister to be appointed by Tuesday to try to defuse the country's political crisis.
Grand Ayatollah Sistani said key positions should be agreed before the new parliament meets then. Pressure has been building for a national unity government.
Prime Minister Nouri Maliki wants a third term, though correspondents say he is seen by many as having precipitated the crisis through sectarian policies that have pushed Iraq's Sunni minority into the hands of Isis extremists.
Meanwhile, the Archbishop of Irbil, in northern Iraq, told the BBC that more than 40,000 Christians had fled villages near Mosul in recent days after insurgents attacked the two large Christian settlements of Karakosh and Karamlaish.
The displaced have sought refuge in the Kurdistan region of Iraq.
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A spokesman for the rebels confirmed heavy fighting but implied the attack had failed, saying they were pursuing what was left of the army offensive.
The rebels control large swathes of the north and west after lightning raids that captured the second city, Mosul.
'Flee or be killed'
On Saturday, thousands of Iraqi troops backed by tanks and air power attacked Tikrit from four directions, state TV said.
It said there had been complete success in clearing Isis from the city, with some militant commanders among the 60 killed. It said the other insurgents there had fled.
Tikrit fell on 11 June to rebels of the Islamic State in Iraq and the Levant (Isis).
The BBC's Jim Muir, who is in northern Iraq, says that since then, the government has been threatening a counter-offensive from the next town down the Tigris river - Samarra - where the insurgents were finally checked.
State TV said preparations were now being made to move north towards Mosul.
The Iraqi soldiers are being supported in the offensive by allied Sunni tribesmen and Shia militias.
The attack on Tikrit included air strikes that targeted insurgents at a university campus to the north of the city.
Soldiers had captured part of the campus in a helicopter operation on Friday.
Army spokesman Lt-Gen Sabah Fatlawi had warned Isis fighters they "now have two choices - flee or be killed".
One Tikrit resident, Yousef, told the BBC there was still fighting in the city, in both northern and southern districts.
He said: "Most residents have already left Tikrit. Most have left for Kirkuk or Mosul. They are scared of being stuck in the middle of all the fighting. Only five families in my street have stayed."
Iraqi military sources said the offensive on Tikrit - the mainly Sunni hometown of former leader Saddam Hussein - was being co-ordinated with American military advisers.
However, although the US has confirmed it is flying armed drones in Iraq to protect US personnel on the ground, US officials say American troops are not directly involved in the hostilities.
Some 300 US military advisers have been deployed to Iraq.
Also on Saturday, fighting to the south of the capital Baghdad left at least 20 Iraqi troops dead. Police officials told AP dozens of insurgents were also killed.
Another army spokesman told Agence France-Presse that Iraqi forces were also now in control of a key road from Baghdad to Samarra.
Separately, Iraq's most influential Shia cleric called for a prime minister to be appointed by Tuesday to try to defuse the country's political crisis.
Grand Ayatollah Sistani said key positions should be agreed before the new parliament meets then. Pressure has been building for a national unity government.
Prime Minister Nouri Maliki wants a third term, though correspondents say he is seen by many as having precipitated the crisis through sectarian policies that have pushed Iraq's Sunni minority into the hands of Isis extremists.
Meanwhile, the Archbishop of Irbil, in northern Iraq, told the BBC that more than 40,000 Christians had fled villages near Mosul in recent days after insurgents attacked the two large Christian settlements of Karakosh and Karamlaish.
The displaced have sought refuge in the Kurdistan region of Iraq.
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