His death was announced by the AQAP group in an online video. His successor was named as military chief Qasim al-Raymi.
Wuhayshi was seen as al-Qaeda’s second-in-command and was a former private secretary to Osama Bin Laden, the BBC reports.
He built one of the most active al-Qaeda branches, U.S officials said.
In Yemen, resurgent al-Qaeda militants have seized territory and infrastructure – indirectly assisted by Saudi-led air strikes on the rebel Houthi movement, their Shia Muslim foes.
But the deaths of a number of leading figures in AQAP in recent months have reportedly fuelled rumours among supporters that it has been successfully targeted by intelligence agencies.
The Yemeni news group al-Masdar Online previously reported (in Arabic) that Wuhayshi was killed in an attack in Hadramawt province last Friday.
“We in al-Qaeda in the Arabian Peninsula mourn to our Muslim nation that Abu Baseer Nasser bin Abdul Karim al-Wuhayshi, may God have mercy on his soul, passed away in an American strike which targeted him along with two of his mujahideen brothers,” Khaled Batarfi, a senior member of the group, said in the video.
The Pentagon has previously said it would not comment on the killing – which the Site intelligence group has said would constitute the biggest strike on al-Qaeda since Bin Laden’s death in Pakistan in 2011.