"The shura council of al-Qaida in Iraq unanimously agreed on Sheik Abu Hamza al Muhajir to be a successor to Sheik Abu Musab al Zarqawi," said a statement on a Web site the group often uses to issue statements.
"Sheik Abu Hamza is a pious brother with a jihad track record and a solid scholarly background. We ask God to bless him and to help him finish what Sheik Abu Musab has started," the statement said.
The Jordanian-born Zarqawi was killed when a U.S. air strike dropped two 500-pound bombs on a house where he was hiding. Five of his aides also died in the blast.
Sky News said Zarqawi gave away his whereabouts in a recent video, when intelligence agents were able to identify the desert and shrubs in the background.