Hundreds of Peshmerga fighters, backed by artillery and US-led coalition air strikes, advanced on Bashiqa from three directions on Monday morning.
By late afternoon, they were moving from house to house clearing the town, a Peshmerga statement said.
Meanwhile, the Iraqi military said it had found a mass grave filled with some 100 decapitated bodies south of Mosul.
The grave was located in the grounds of an agricultural college on the outskirts of the town of Hamam al-Alil, which troops entered over the weekend.
"Specialised teams will be sent to investigate this heinous crime," the military said.
IS militants have carried out many mass killings in the past, boasting about them in photos and videos circulated online.
In 2014, they targeted security forces personnel and members of ethnic and religious minorities as they swept across northern Iraq after taking control of Mosul.
The UN has also received reports that militants have carried out atrocities since the Iraqi government's offensive to retake Mosul began three weeks ago.
On 29 October, they are alleged to have killed 40 former soldiers from the Hamam al-Alil and Shura areas, and thrown their bodies into the River Tigris.
Bashiqa, about 12km (8 miles) from Mosul, was surrounded by Peshmerga fighters two weeks ago as part of the wider Mosul offensive.
At about 06:00 (03:00 GMT) on Monday, the operation to finally clear the town got under way.
By 17:00, the Peshmerga had advanced into the town and begun house-to-house clearances, a statement by their general command said.
A senior Peshmerga officer, Brig-Gen Musa Gardi, told the Kurdish news agency Rudaw that pockets of militants remained that would be dealt with soon.
He also warned that they might use tunnels and suicide bombs to launch attacks.
About 40 car bombs targeted Peshmerga positions on Monday alone, he added.
Rudaw earlier posted a video showing what it said was a bus packed with explosives that was destroyed in a coalition air strike on the edge of Bashiqa.
Iraqi special forces and army units meanwhile continued operations to clear eastern districts of Mosul, six days after entering the last major IS urban stronghold in Iraq.
Their progress has been slowed by suicide car bombs, booby traps and the need to engage in house-to-house fighting along narrow streets.
The US special envoy to the multinational coalition against IS, Brett McGurk, nevertheless declared late on Sunday that the offensive was "very much on track".
"Everything in Mosul is ahead of schedule on all axes of advance but Daesh, as we expected, is putting up a fierce fight and I expect this will take some time to conclude," he said, using a pejorative term for IS based on the acronym of a previous name in Arabic.
Mr McGurk also outlined how he expected the operation to retake the IS-held northern Syrian city of Raqqa, launched by a US-backed alliance of Syrian Kurdish and Arab fighters earlier on Sunday, would proceed in "very deliberate phases".
"There is an isolation phase which began today, and there will be subsequent phases to make sure that that we kick [IS] out of Raqqa," he added.
Iraqi Kurdish forces have fought their way into a town held by Islamic State militants north-east of Mosul.