The breakthrough comes after the US carried out air strikes overnight on Islamic State (IS) positions near the town.
The mayor of Amerli and army officers said troops backed by militias defeated fighters from the IS to the east of the town.
Fighting is understood to have continued to the north of Amerli. Fifteen Islamic State fighters were said to have been captured.
“Security forces and militia fighters are inside Amerli now after breaking the siege and that will definitely relieve the suffering of residents,” said Adel al-Bayati, mayor of Amerli.
The advance of the Iraqi forces comes after the US military carried out air strikes overnight on IS positions near the town and airdropped humanitarian supplies to trapped residents.
More aid was dropped from British, French and Australian planes.
Some 15,000 minority Shia Turkmen in Amerli have been surrounded by IS militants for two months.
“I can see the tanks of the Iraqi army patrolling Amerli’s street now. I’m very happy we got rid of the Islamic State terrorists who were threatening to slaughter us,” said Amir Ismael, an Amerli resident.
Armed residents had managed to fend off attacks by IS fighters, who encircled the town whose majority Shiite Turkmen population it regards as apostates.
More than 15,000 people had remained trapped inside Amerli.
IS has captured large areas of northern Iraq since June. Earlier this month, the militant group dealt a bruising defeat to Kurdish forces and threatened to enter their semi-autonomous region, prompting US air strikes.
Reports described it as the biggest military operation since IS began making major gains in Iraq in June.
The UN had expressed fears there could be a massacre if IS took the town, which lies in the Kurdish region of Iraq.
IS has been accused of atrocities in parts of Iraq and Syria under its control.
IS has also seized large swathes of territory in Iraq and Syria in recent months, including Iraq’s second city, Mosul.
Pledging allegiance to their leader, Abu Bakr al-Baghdadi, the jihadists have imposed a harsh form of Islamic rule in areas under their control.
The group has declared a new caliphate, an Islamic state ruled by a religious leader, and Abu Bakr al-Baghdadi has declared himself caliph.
The IS ideology has attracted would-be jihadists from a number of western nations, including the UK, and has spread its message aggressively on social media, often posting gruesome pictures of beheadings and mass killings.
The group responded to the US carrying out air strikes against it by killing an American journalist, James Foley, on 19 August.