In a statement distributed by the group's supporters, Amaq News Agency reported that Abu Muhammad al-Adnani died in the city of Aleppo.
He was "martyred while surveying the operations to repel the military campaigns against Aleppo", it said.
Adnani was known for his calls for lone-wolf attacks in the West.
One of the group's founder members, he is also said to have masterminded attacks in Europe and elsewhere.
The statement did not say how Adnani - who had a US bounty of $5m (Â£3.82m) on his head - was killed.
Hisham al-Hashimi, a security analyst who advises the Iraqi government on IS, said Adnani was injured in a US-led coalition strike on 17 August north of Aleppo, where IS is fighting Turkish- and US-backed Syrian rebels.
Mr Hashimi said he died from his wounds on Monday.
Islamic State group - the full story
His death comes at a time when IS is suffering military reverses in both Syria and Iraq.
He was last heard in an audio message in May urging Muslims to carry out attacks in the West.
Adnani was born Taha Sobhi Falaha in the northern Syrian town of Banash in 1977.
US officials say he was one of the first foreign fighters to oppose the presence of US-led forces in Iraq after the 2003 invasion.
One of the longest-serving and most prominent leaders of so-called Islamic State (IS) has been killed in Syria, IS-affiliated media say.