"As emir of Al-Qaeda, I pledge to you our allegiance, following the path of Sheikh (Osama) bin Laden and his martyred brothers in their allegiance to Mullah Omar," Zawahiri said, referring to the former Al-Qaeda leader and to the longtime Taliban chief whose death was confirmed last month.
The statement came amid a bitter struggle within the Taliban over Mansour's leadership.
The recording was featured in a video that opens with images of bin Laden - who was killed by US special forces in Pakistan in 2011 - pledging allegiance to Omar.
He says that the "Islamic emirate" established by the Taliban in Afghanistan was the "first legitimate emirate after the fall of the Ottoman Empire, and there is no legitimate emirate in the world apart from it."
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He pledged to Mansour to "implement sharia law" and to continue "jihad until every part of occupied Muslim land is free."
Mansour was announced as the new Taliban chief on July 31, after the movement confirmed the death of Omar, who led Islamist insurgency for some 20 years.
Zawahiri's pledge also comes as Al-Qaeda faces a growing rivalry with the Islamic State group, which has seized control of larges parts of Syria and Iraq, for preeminence in the global jihadist movement.