The Popular Mobilisation, a paramilitary group, said that it and the security forces had killed Bilal Omar Bakri.
He was "leading a group that tried to attack one of our units," in Salaheddin north of Baghdad, according to a statement from the group, dominated by Tehran-backed Shiite militias.
A Lebanese security source confirmed that Bilal Omar Bakri, who was in his late 20s, had been killed "fighting in the ranks of IS" in Salaheddin province.
Another of the preacher's sons, Mohammad Omar, who was in his late 30s, died fighting for IS in Aleppo in Syria several months earlier, the source told AFP on condition of anonymity.
Omar Bakri, who holds Lebanese citizenship, became known in Britain for supporting Al-Qaeda.
A security source said that he was sentenced in October to six years of hard labour for establishing an organisation affiliated with the jihadist Al-Nusra Front in Syria and establishing training camps for it in Lebanon.
When he was based in London, the Sunni firebrand was known in the media as the "Tottenham Ayatollah" despite the term applying to a high rank in the Shiite clergy.
Omar Bakri fled Britain, where he lived for two decades, to Lebanon after praising the perpetrators of the September 11, 2001 attacks in the United States and the July 7, 2005 bombings in London.
He had most recently been arrested in May 2014 for his involvement in unrest in the northern city of Tripoli.
He has denied any links to Al-Qaeda although he said he believed "in the same ideology".
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