Sinai Province, which has waged an insurgency against the Egyptian state, posted pictures of around two dozen fighters standing among trees, with a caption saying they were pledging allegiance to Abu Ibrahim al-Hashemi al-Quraishi.
Quraishi was named on Thursday in an audio message that also confirmed Baghdadi's death and vowed revenge against the United States. U.S. special forces killed Baghdadi in a raid in northwest Syria.
Islamic State has resorted to guerrilla attacks since losing its last significant piece of territory in Syria in March, and has posted dozens of claims of responsibility for attacks in several countries since Baghdadi's death.
Conflict in Egypt's Sinai Peninsula escalated after President Mohamed Mursi of the Muslim Brotherhood was toppled by the military in 2013.Egyptian ground and air forces launched a major offensive focused on North Sinai early last year. Military operations and militant attacks continue in the area.