Al-Wuhayshi was the top leader of al Qaeda in the Arabian Peninsula, or AQAP, one of the most dangerous and dynamic branches of the jihadist network.
Al-Wuhayshi was al Qaeda's "leading light" and was one day expected to take over from its current global chief, Ayman al-Zawahiri
, said Cruickshank.
Two Yemeni security officials told CNN on Monday that al-Wuhayshi was killed Friday in a suspected U.S. drone strike in Yemen's Hadhramaut region.
On Tuesday, AQAP released a video statement announcing that its leader and two aides had died. The speaker said that al-Wuhayshi would be succeeded by the group's military chief, Qasm al-Rimi, also known as Abu Hureira al-Sanaani.
The U.S. government confirmed al-Wuhayshi's fate Tuesday, calling his death "a major blow to (al Qaeda's) most dangerous affiliate and to al Qaeda more broadly."
Al-Wuhayshi "was responsible for the deaths of innocent Yemenis and Westerners, including Americans," U.S. National Security Council spokesman Ned Price said.
"While AQAP, al Qaeda and their affiliates will remain persistent in their efforts to threaten the United States, our partners and our interests, (al-Wuhayshi's) death removes from the battlefield an experienced terrorist leader and brings us closer to degrading and ultimately defeating those groups."
Al-Wuhayshi, known as al Qaeda's crown prince, was a charismatic figure who was adored by many of the terrorist group's jihadist fighters.
In a video that surfaced in April of last year, al-Wuhayshi appeared brazenly out in the open
, greeting followers in Yemen, the impoverished nation that the organization uses as a base.
In a speech to the group, he makes it clear that he's going after the United States, saying: "We must eliminate the cross. ... The bearer of the cross is America!"
The video showed what looked like the largest and most dangerous gathering of al Qaeda in years.
Successor seen as 'brains of the operation'
Originally from Yemen
, al-Wuhayshi assumed command of AQAP in 2009. He'd escaped a Yemeni prison in 2006 and had previously worked as a personal secretary for Osama bin Laden
His successor is also seen as a formidable leader.
"Qasm al-Rimi was considered the brains of the operation," Cruickshank said. "For more than a decade, he's really been at the helm of the military side of things for AQAP but also planning their large international operations."
The leadership change is expected to bring "a degree of continuity," he said, noting that al-Wuhayshi and al-Rimi were believed to have worked very closely together.
AQAP benefiting from Yemen chaos
Al-Wuhayshi's death comes at a time when AQAP appears to have been thriving amid the recent turmoil in Yemen.
The group has been "expanding the territory they control, taking advantage of political chaos," Cruickshank said.
AQAP has been feeding off anger among Sunni tribes in Yemen over the advances made by the predominantly Shiite Houthi rebels who overthrew the Yemeni government earlier this year.
Adding to the violence and destruction, a Saudi-led coalition has been bombing the Houthis and their allies in an effort to restore the deposed government.
AQAP has exploited the unrest to seize more turf, including the port city of Al Mukalla, where it freed hundreds of inmates from a prison in April.
The Yemeni security officials told CNN that the drone strike that killed al-Wuhayshi took place in southern Al Mukalla.
'This is a long, difficult struggle'
Yemen's descent into chaos prompted the United States to pull out its Special Operations forces
based in the country in March, raising fears that its counterterrorism efforts against AQAP would be hobbled.
But al-Wuhayshi's death and an airstrike in April
that killed a senior AQAP leader show that Yemen is no haven for the terrorist group.
U.S. Sen. Angus King, an independent from Maine, told CNN on Monday that the terrorist leader's death would hurt al Qaeda, but he stressed that the jihadist network still poses a threat.
"This is a long, difficult struggle that we're engaged in, and it's going to require all kinds of tools," he said.
News of al-Wuhayshi's death emerged days after U.S. planes carried out a strike inside Libya, purportedly killing a key terror figure in North Africa.
The target was Mokhtar Belmokhtar, a veteran Islamist fighter who is blind in one eye and affiliated with al Qaeda in North Africa, a U.S. official told CNN.
The Libyan government said Belmokhtar was killed in the weekend strike, something that U.S. officials have not confirmed.