According to the IS-controlled Amaq news agency, Abu Ibrahim al-Hashemi al-Qurayshi has been chosen as a new leader.
US special forces tracked down Baghdadi in north-west Syria at the weekend and attacked his compound.
The IS leader fled into a tunnel and killed himself and two children using a suicide vest.
Baghdadi was declared leader of the extremist group in 2014 when IS took control of huge swathes of Iraq and Syria and imposed its rule over the civilian population.
In an audio message released on messaging service Telegram, IS also confirmed the death of spokesman Abu al-Hasan al-Muhajir – who was killed in a separate joint US-Kurdish operation on 27 October.