Nadhari and three other militants were killed in a January 31 "crusader American drone strike against their car" in Shabwa province of southern Yemen, Al-Qaeda in the Arabian Peninsula said on Twitter.
AQAP named the three others as Said Bafaraj, Abdelsamie al-Haddaa and Azzam al-Hadrami.
Tribal sources had said four suspected militants were left charred in their car in a drone strike that day in Shabwa.
Nadhari had threatened France with further attacks like those in Paris on satirical magazine Charlie Hebdo and a Jewish supermarket that killed 17 people between January 7 and 9.
Another of the group's ideologues, Nasser bin Ali al-Ansi, claimed the attack on Charlie Hebdo on behalf of AQAP four days later.
Despite a political crisis in Yemen, US President Barack Obama on January 25 vowed no let-up in Washington's campaign against jihadists in Yemen.
He ruled out a US troop deployment in Yemen but said Washington would continue "to go after high value targets inside Yemen".
Western governments say it remains unclear if AQAP directly orchestrated the Charlie Hebdo attack, although they do believe one or both of the attackers, brothers Said and Cherif Kouachi, spent time with jihadists in Yemen.
AQAP was formed in 2009 after a merger between militants in Yemen and Saudi Arabia.
According to the New America Foundation, the United States has carried out more than 110 strikes on targets in Yemen since 2009, mostly using drones.
In September 2011, a drone strike killed US-Yemeni cleric Anwar al-Awlaqi, the AQAP leader accused of instigating a string of attacks against the United States.
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