In the video entitled 'Days With The Imam', uploaded to a radical Islamist website, al-Zawahiri also reveals that bin Laden was a one-time member of the Muslim Brotherhood.
The Muslim Brotherhood is Arab world's most influential and one of the largest Islamic movements, and is also the largest political opposition organisation in many Arab states.
Zawahiri revealed "for those who do not know" that Saudi-born bin Laden was left blind in his right eye after an accident during his youth.
He also claimed that the terrorist mastermind was expelled from the Saudi branch of the Muslim Brotherhood for insisting on waging jihad, holy war, against the Soviet Union in Afghanistan, the Daily Mail reported.
It is claimed that bin Laden travelled to the Pakistani city of Peshawar, near the border with Afghanistan, to deliver cash to the Taliban, but then defied the Brotherhood's orders to join the armed struggle.
Zawahiri's latest video posted on a jihadist forum appeared to be around two months old as he offered greetings to Muslims for the start of the fasting month of Ramadan which ended on Aug 20.
Earlier this month, Zawahiri's brother Mohamed 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.
Speaking on the eve of the anniversary of the 9/11 terror attacks, Mohamed al-Zawahiri said he and his brother are ideologically inseparable.
"Our people like death, the same way others like life," he told reporter Nic Robertson. "But we do not want to get into this endless cycle of violence. We like for others and us to live peacefully," he had said.
Later he said, "The portrayal of my brother's ideologies and mine: That it's blood thirsty, barbaric, or terrorist, is not true at all."
Bin Laden was killed on May 2, 2011 by US commandos in a daring night raid in Abbottabad.