The man who called himself "Muslim bin John" was born in New Zealand and had been attending "some sort of terrorist training camp" in Yemen, Key said.
"I was advised it was highly likely he was killed in the latter part of 2013 but it took some time to confirm that through DNA," he told reporters.
The Australian newspaper said that the man died in a US Predator drone strike on five Al-Qaeda militants travelling in a convoy of cars in Yemen in November.
Key confirmed the deaths were the result of a drone strike and said New Zealand had no prior knowledge of the operation.
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He defended the use of drones, saying: "They are legitimate at certain times, where countries are trying to contend with dangerous situations and they're trying to deal with terrorists without putting their own people in harm's way."
Asked if this specific drone strike was legitimate, he replied: "I suspect so yes, given that three of the people killed were well-known Al-Qaeda operatives."
"We understand the men were killed during a counter-terrorism operation and do not intend to discuss its details," a spokeswoman said.
Police and consular officials in Australia and New Zealand were in contact with the next of kin when the deaths were confirmed and the Australian Federal Police helped in identifying the remains, she said.
The Australian newspaper said US officials notified their Australian counterparts about the possibility its citizens had been "collateral damage" in the strike on November 19.
However, they were "foot soldiers" for Al-Qaeda in the Arabian Peninsula (AQAP) who may have been involved in kidnapping westerners for ransom, the report said, quoting an unnamed source.
At the time, Yemeni authorities said that a drone strike in Hadramawt province killed three Al-Qaeda suspects when a missile hit their vehicle.