The group named Abu Ibrahim al Hashimi al Quraishi as its new leader, according to a statement distributed by the group's media wing.
Daesh confirmed the death of its leader Abu Bakr al Baghdadi in a statement on Thursday and named his replacement as Abu Ibrahim al Hashimi al Quraishi.
"We mourn you... commander of the faithful," said Abu Hamza al Quraishi – presented as the terrorist group's new spokesman – in an audio statement.
Baghdadi, who led Daesh since 2014 and was the world's most wanted man, was killed in a US special forces raid in Syria's northwestern province of Idlib on Sunday.
The group also confirmed the killing in another raid the following day of the group's previous spokesman Abu Hassan al Muhajir.
The statement said Daesh's legislative and consultative body convened after the 48-year-old Iraqi-born terrorist chief's death.
"The Islamic State [Daesh] shura council convened immediately after confirming the martyrdom of Sheikh Abu Bakr al Baghdadi, and the elders of the holy warriors agreed" on a replacement, said the seven-minute message.
Little is known about Hashimi, whose name was seldom mentioned as a possible successor the multiple times that Baghdadi was reported killed in recent years.
"We don't know much about him except that he is the leading judge of IS [Daesh] and he heads the Sharia committee," said Hisham al Hashemi, an Iraqi expert on Daesh.
The Daesh spokesman also issued a stark warning to the United States, whose President Donald Trump announced Baghdadi's death in a televised address from the White House.
'Crazy old man'
"He died after running into a dead-end tunnel, whimpering and crying and screaming all the way," Trump said on Sunday, adding that Baghdadi "died like a dog".
In the new audio message, the new Daesh spokesman described Trump as "a crazy old man" and warned the US that the group's supporters would avenge Baghdadi's death.
"Do not rejoice America," he warned, "the new chosen one will make you forget the horror you have beholden... and make the achievements of the Baghdadi days taste sweet".
The spokesman also referred to an earlier call by Baghdadi for the thousands of Daesh terrorists held in Syrian and Iraqi prisons to be freed.
Most of those prisoners are Iraqi and Syrian but the detainees also include more than 2,000 foreigners who hail from more than 50 different countries.
With aerial and logistical assistance from an international coalition led by the US, Iraqi and Syrian forces have wrested back all the territory lost to Daesh in 2014.
US president Trump announced that Daesh has been fully destroyed.