He was known as Muslim bin John and was killed alongside three others, one of them an Australian, Mr Key told reporters on Wednesday.
“We had known for some time that he was in Yemen,” Mr Key said.
“Late last year I was advised it was highly likely he had been killed; it took some time to absolutely confirm that through DNA.”
Mr Key says the man was born in New Zealand and has family there.
His real name won’t be released.
“He was known as Muslim bin John,” Mr Key said.
“I know there has been some discussion about whether his name was Mark Taylor – I wouldn’t normally get into this, but as the press has run it, it’s not Mark Taylor.”
The drone strike was on a convoy of cars in Hadramout on November 19, The Australian newspaper reports.
Mr Key said in his view the drone strike was legitimate.
“I think drones are legitimate at certain times when countries are contending with dangerous situations, and they’re trying to deal with terrorists without putting their own people in harm’s way,” he said.
“I suspect this was one of those times.”
Green Party co-leader Russel Norman doesn’t think it was legitimate.
“Having a government of the United States going around and assassinating people I think fundamentally undermines our freedom,” he said.
“I think it shows the United States thinks that it has free reign to assassinate people that it doesn’t like.”
Dr Norman said he was concerned the Government Communications Security Bureau was “in some way complicit” and might have provided information connected with the strike.
“If we’re going to deal with terrorism, we can’t act like terrorists, we actually need to obey the rule of law.”