There has been no official confirmation of reports that Abu Bakr al-Baghdadi was killed in the raid. He has been wrongly reported dead on several previous occasions.
US President Donald Trump is due to make a “major statement” at 1300 GMT.
Mr Trump earlier tweeted: “Something very big has just happened!”
A villager in the village of Barisha in Idlib province, north-west Syria, described to the BBC a dramatic military operation late on Saturday night.
He said helicopters had launched an assault that lasted 30 minutes, firing missiles at two houses and flattening one, before troops became active on the ground.
The commander of the Kurdish-led Syrian Democratic Forces (SDF), Mazloum Abdi, said on Sunday that a “historic, successful operation” had resulted from “joint intelligence work” with the US.
Turkey has also said it co-ordinated with the US military ahead of the operation, describing it as “a good day for the good guys”.
The raid was carried out by US special operations forces after they received “actionable intelligence”, Newsweek said, citing unnamed sources.
The Syrian Observatory for Human Rights, a UK-based monitoring group, said…