Quraishi was named as the organization’s leader on Thursday in an audio message that also confirmed Baghdadi’s death and vowed revenge against the United States.
US special forces killed Baghdadi in a raid in northwest Syria last month.
His death is likely to cause ISIS to splinter, leaving whoever emerges as its new leader with the task of pulling the group back together as a fighting force, according to analysts.
ISIS has resorted to guerrilla attacks since losing its last significant piece of territory in Syria in March.
Since Baghdadi’s death, it has posted dozens of claims of responsibility for attacks in Iraq, Syria, Afghanistan and elsewhere.