"The general command of al-Qaeda announces, after consultations, the appointment of Sheikh Ayman al-Zawahiri as head of the group," the statement, posted online on Thursday, said.US special forces killed bin Laden in a raid on the Pakistani city of Abbottabad on May 2.
Al-Qaeda under the new leadership of al-Zawahiri will pursue its fight against the US and Israel, the group said in the statement.
"We seek with the aid of God to call for the religion of truth and incite our nation to fight ... by carrying out jihad against the apostate invaders ... with their head being crusader America and its servant Israel, and whoever supports them," it said.
Al-Zawahiri has been al-Qaeda's number two for years.
$25m reward for whereabouts of Al-Zawahiri
His whereabouts are unknown but he is widely believed to be hiding along the border between Afghanistan and Pakistan. The United States is offering a $25m reward for any information leading to his capture or conviction.
"Only a few weeks ago when the US Secretary of State Hillary Clinton was here in Pakistan she reportedly gave Pakistan what's been described as a hitlist", Al Jazeera's Imtiaz Tyab, reporting from Islamabad, said.
"It listed five names and Zawahiri's name was on the list. Whether that means the new al-Qaeda leader is here we don't know for sure, but it certainly raises some questions".
Believed to be in his late 50s, al-Zawahiri met bin Laden in the mid-1980s when both were in Pakistan to support fighters battling the Soviet Union in Afghanistan.
Al-Zawahiri, who was born in Egypt, vowed earlier this month to press ahead with al-Qaeda's campaign against the US and its allies, in what appeared to be his first public response to bin Laden's death.
"The Sheikh [bin Laden] has departed, may God have mercy on him, to his God as a martyr, and we must continue on his path of jihad to expel the invaders from the land of Muslims and to purify it from injustice," he said in a video message posted online.
"Today, and thanks be to God, America is not facing an individual or a group ... but a rebelling nation which has awoken from its sleep in a jihadist renaissance challenging it wherever it is."
In Thursday's statement, al-Qaeda voiced its "support [to] the uprisings of our oppressed Muslim people against the corrupt and tyrant leaders who have made our nation suffer in Egypt, Tunisia, Libya Yemen, Syria and Morocco."
The group urged those involved in the uprisings to continue their "struggle until the fall of all corrupt regimes that the West has forced onto our countries."
But Al Jazeera's Ayman Mohyeldin, reporting from Cairo where a popular uprising toppled longtime President Hosni Mubarak in February, said the so-called "Arab Spring" has undermined al-Qaeda in many Arab countries.
"This has been a significant blow to the ideology of al-Qaeda", he said. "Many believe al-Qaeda has lost a great deal of momentum and support across the Arab world because these revolutions were able to deliver change without the use of violence."
