The announcement comes a day after an Iraqi official declared that Iraq's Diyala Province had been "liberated" from ISIS.
Idriss Nassan, Kobani's deputy foreign minister, told CNN he expects an official announcement Tuesday "if things continue this way."
"YPG is in control," Nassan said, using the acronym for the People's Protection Units. "They are making sure to clear the streets and the places from ISIS to declare it a free city."
YPG spokesman Polat Can confirmed the news in a tweet: "Congratulations for liberation of Kobani to all of humanity, Kurdistan and people of Kobani."
Nassan called for the quick implementation of a "humanitarian corridor" to help the myriad refugees in the city, whom, he said, "need everything."
A Kobani official, who did not want to be named because it would interfere with Tuesday's official announcement, said the Kurds were going house to house in the newly liberated area to check for booby traps. Once the traps are removed or defused, the fighters will invite residents to return to their homes, the official said.
According to London-based opposition group, the Syrian Observatory for Human Rights -- which also confirmed Kobani was liberated -- since October 6, when ISIS first raised its banner on the city's outskirts, the fighting among ISIS, YPG and the rebel battalions backing YPG has killed 979 ISIS combatants, 324 YPG fighters and 12 rebels.
Thirty-eight more ISIS militants died in attacks using booby-trapped vehicles or explosive belts, and the ISIS shelling of Kobani killed 12 civilians, SOHR said.
"On the other hand, hundreds of (ISIS) militants died during U.S. and Arab allies' airstrikes on the city and its countryside. Meanwhile, large parts of the city have become uninhabitable due to U.S. and Arab allies air raids, detonation of booby-trapped vehicles and mutual shelling," the group said.
Kobani apparently declared itself autonomous exactly one year before Monday's victory, SOHR said.
Iraqi victory claimed over ISIS in Diyala
A large-scale military operation to reclaim Iraq's Diyala Province from ISIS was successful, Iraqi transportation minister Hadi al-Amiri said Sunday.
The operation started last week, and at least 58 people -- including two journalists -- were killed. Nearly 300 others were wounded.
In a televised news conference Sunday, al-Ameri, who is also the head of the a powerful Shiite militia, said the province was "liberated" from ISIS.
Al-Amiri said that Iraqi security forces are searching for ISIS militants who fled into orchards and farms in remote areas.
Diyala Police commander Brig. Gen. Jamil Kamel al-Shamari also announced that Diyala is now under full control of Iraqi security forces.
ISIS has been fighting for Kobani for months, hoping to add it to the territory it already controls in Syria and Iraq as part of what it calls its independent Islamic nation.
Syria has been embroiled in a more than three-year civil war, with government troops battling ISIS and other rebels elsewhere, leaving Kobani's ethnic Kurds to defend the city.
Kobani, aka Ayn al-Arab, is strategically important because of its location on the border with Turkey.
Airstrikes by the United States and its allies, part of a larger U.S.-led coalition effort against ISIS in the region, intermittently take out ISIS targets in the area. The coalition started operations in September.