IS's bloody attack on the town had left at least 174 civilians dead as well as 70 combatants, the Syrian Observatory for Human Rights said.
"The Kurdish People's Protection Units (YPG) took back control of IS positions in Kobane," the Britain-based group said.
"The YPG were able to take back the town's boys' high school, where the last of the IS fighters were holed up, after setting off explosions."
The jihadist group entered Kobane at dawn on Thursday, seizing several buildings in the town's south and southwest.
Local journalist Rudi Mohammad Amin told AFP that "all of Kobane is again under the control of the YPG."
"The YPG detonated explosives outside of the school, then stormed it," Amin said, speaking via the Internet from a position near Kobane.
"This military operation was carried out after ensuring that there were no civilians left in the school," he added.
Amin said he believed all the IS fighters in the school were killed.
According to the Observatory, which monitors the war in Syria through a network of contacts on the ground, YPG fighters and members of the Kurdish security forces were searching the town for any remaining jihadists.
At least 16 Kurdish fighters were killed and 54 jihadists.
Observatory director Rami Abdel Rahman, said the death toll was still mounting as Kurdish forces discovered more bodies.
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