He was killed in a counter-terrorism operation carried out by the CIA in the Afghan capital of Kabul on Sunday.
Mr Biden said Zawahiri had "carved a trail of murder and violence against American citizens".
"Now justice has been delivered and this terrorist leader is no more," he added.
Officials said Zawahiri was on the balcony of a safe house when the drone fired two missiles at him.
Other family members were present, but they were unharmed and only Zawahiri was killed, they added.
Mr Biden said he had given the final approval for the "precision strike" on the 71-year-old al-Qaeda leader after months of planning.
Zawahiri took over al-Qaeda after the death of Osama bin Laden in 2011. He and Bin Laden plotted the 9/11 attacks together and he was one of the US's "most wanted terrorists".