Zawahiri made the claim in an hour-long video titled "Days With The Imam" that was uploaded on a radical Islamist website, the Daily Mail reported.
Osama was killed in a US Navy Seal raid on his compound in Pakistan's Abbotabad city last year.
In the video, Zawahiri said Osama was also a one-time member of the Muslim Brotherhood.
Zawahiri revealed that "for those who do not know" the Saudi-born bin Osama was left blind in his right eye after an accident during his youth, the British daily said.
He also said Osama was expelled from the Saudi branch of the Muslim Brotherhood for insisting on waging jihad - or holy war - against the Soviet Union in Afghanistan.
Osama travelled to Pakistan's Peshawar cityy to deliver cash to the Taliban, but then defied the Brotherhood's orders to join the armed struggle.
The Daily Mail said that Zawahiri's video may be around two months old as he offered greetings to Muslims on Ramadan that ended Aug 20.
Earlier this month, Zawahiri's brother gave an interview to CNN in which he outlined his personal "peace plan" he said could lead to a rapprochement between Islamists and the West.
Mohamed al-Zawahiri said he and his brother are "ideologically inseparable".
"Our people like death, the same way others like life. But we do not want to get into this endless cycle of violence. We like for the others and us to live peacefully," he told CNN.
"The portrayal of my brother's ideologies and mine - that it's blood thirsty, barbaric, or terrorist - is not true at all," he said.