Bin Laden was killed in a U.S. raid on his compound in Abbotabad, Pakistan, last month.
The statement cannot be authenticated by CNN, but it appeared on radical Islamist sites known for posting similar statements and recruitment videos by other al Qaeda figures.
"Hereby the General Command of the Qaida al-Jihad - and after the end of the consultations -- we declare that Sheikh Dr. Abu Muhammad Ayman al-Zawahiri (May God bless him) will take over the responsibility of command of the group," the statement said.
The statement also said the group will not shift its policy and pledged its support to, among others, Mullah Omar and the Taliban as the latter battles U.S. and NATO presence in Afghanistan.
It, however, makes no mention of the pro-democracy uprisings that have roiled several Arab countries and forced the exit of some longtime leaders.
Born into a wealthy family in Cairo, al-Zawahiri is a physician and founding member of the Egyptian Islamic Jihad (EIJ), a militant organization that opposed the then secular Egyptian government of Hosni Mubarak and sought its overthrow through violent means.
Like bin Laden, al-Zawahiri also went to Afghanistan during their fight against the Soviets, although he was there primarily to offer his medical expertise.
By the 1990s, he again refocused his attention on undermining and attacking the Egyptian government and, eventually, the U.S..
In 1998, when the Egyptian Islamic Jihad effectively merged with al Qaeda, he sent a fax to the Al-Hayat newspaper warning Americans. Three days later on August 7, suicide truck bombers hit the U.S. embassies in Nairobi, Kenya and Dar es Salaam, Tanzania, killing 224 people.
The FBI is offering a $25 million reward for information leading to his capture -- the same as the reward for bin Laden -- reflecting al-Zawahiri's importance to the United States.
Paul Cruickshank, a CNN terrorism analyst, said: "Of all al Qaeda's senior leaders, al-Zawahiri is probably the one in most jeopardy. Western intelligence officers have told us that in recent times bin Laden and al-Zawahiri were probably in relatively close geographic proximity and also in touch to some degree, so all this information may help America track down al-Zawahiri."