Zawahiri, an Egyptian doctor and one of al-Qaida's founders, is wanted by the United States, which is offering a $25 million reward for his capture.
CNN reported the announcement appeared on the radical Islamist sites only Thursday. Ever since bin Laden was killed May 2 by U.S. forces during a raid on his Pakistani compound in Abbottabad, Zawahiri had been widely expected to become al-Qaida's leader.
CNN said while the announcement about Zawahiri could not be authenticated, it appeared on Web sites that usually post such statements and videos of al-Qaida leaders.
"Hereby, the General Command of the Qaida al-Jihad -- and after the end of the consultations -- we declare that Sheik Dr. Abu Muhammad Ayman al-Zawahiri (May God bless him) will take over the responsibility of command of the group," the statement said, warning al-Qaida will not change its direction.
It also pledged support to the Taliban and its spiritual leader, Mullah Mohammed Omar, but made no reference to the pro-democracy uprisings in the Arab world, the report said.
Earlier this month, Zawahiri, in a taped video eulogy for bin Laden, was seen promising to continue the efforts of the terror group's dead leader to "expel the invaders from the land of Islam." In the tape, he also warned of reprisals against the United States.
Zawahiri, who was born into an upper class family of scholars and doctors in Cairo, was No. 2 on the FBI's most-wanted list after bin Laden, al-Arabiya said.
His whereabouts are unknown but his wife and three daughters were believed to have been killed in an airstrike on Kandahar in Afghanistan in 2001, al-Arabiya said.
During the regular press briefing White House spokesman Jay Carney said Zawahiri's accession was not surprising.
"He was identified prior to the successful mission against Osama bin Laden as al-Qaida's No. 2," Carney said. "It's neither surprising nor does it change some fundamental facts, which is al-Qaida's ideology is bankrupt. The fact is that peaceful movements for change are the future of the region and al-Qaida is the past. That was true before Osama bin Laden's death and is true today."