The group identified the new leader as Abu Ibrahim al-Hashimi in the audio released by the IS central media arm, al-Furqan Foundation.
The speaker in the audio also confirmed the death of Abu Hassan al-Muhajir, a close aide of al-Baghdadi and a spokesman for the group.
Al-Muhajir was killed in a joint US operation with Kurdish forces in Jarablus, in northern Syria on Sunday, hours after al-Baghdadi blew himself up during a US raid in Syria's northwestern Idlib province.
"We mourn you... commander of the faithful," an audio statement read by Abu Hamza al-Quraishi, presented as the jihadist group's spokesman, said.
Quraishi also urged followers to pledge allegiance to the new Caliph and addressed the Americans saying: "Don't rejoice."
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The operation on Baghdadi by US special forces in Syria took place Saturday, culminating in the death of the fugitive leader who at his peak headed an organisation that attempted to set up a hardline Islamic state across a huge area of Iraq and Syria.
The Pentagon released video and photos on Wednesday of the US special forces raid that resulted in Baghdadi's death.
Among the images released by the Defense Department was grainy black-and-white footage of US troops approaching on foot the high-walled compound in northwestern Syria where Baghdadi was holed up.
Before and after pictures of the isolated compound were also released.
The compound was razed by US munitions after the raid, leaving it looking like "a parking lot with large potholes," said Marine Corps General Kenneth McKenzie, commander of US Central Command.
McKenzie said that despite Baghdadi's death, IS remains "dangerous."
"We're under no illusions that it will go away just because we killed Baghdadi," he said. "It will remain."
Read more: Baghdadi may be dead, but the turmoil he thrived in lives on
US forces killed a "large number" of IS militants during the raid which culminated in cornering Baghdadi in a tunnel, where he set off a suicide vest.
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