The operation on Tuesday is part of a two-and-a-half week long Iraqi offensive aimed at taking back the city, which fell to rebels led by the Islamic State in Iraq and Levant (ISIL) group in June.
Iraqi state TV said security forces had successfully expelled rebels from the city and were in "complete control" of the area. Al Jazeera's Imran Khan, reporting from Baghdad, said officials were "very confident" about the claim.
Since the start of the rebellion led by the ISIL in June, both the government and the fighters have made conflicting claims of control over several towns, which are difficult to independently verify.
The army has been saying for a fortnight that its forces are on the outskirts of the city, which lies 160km north of Baghdad.
The city is a stronghold of loyalists of former dictator, Saddam Hussein, and ex-army officers who joined forces with the ISIL to take over large parts of north and west Iraq last month.
Iraqi soldiers told Reuters that the military attacked from the village of Awja, about 8km south of the city.
The army retook Awja, the birthplace of Saddam, on the night of July 3, and has been trying to push north since.
Heavy fighting broke out in the Shishin district of southern Tikrit, they said.