"I regret not disclosing this when I had the opportunity to do so," Air Marshal Tony Davies said in a statement on Friday.
He did not elaborate on the circumstances of the relationship or when it happened.
Davies joined the country's air force in 1984 and became chief of the New Zealand Defence Force in 2024.
The military said leadership was transitioning to its deputy chief, Rear Admiral Mat Williams.
"The resignation is for personal reasons, and results from errors of judgement made by me in the past, for which I am taking responsibility," Davies said.
"The errors of judgement were contrary to the values of the defence force."
The military said in a statement that it would not comment further.
The matter has been referred to an independent inspector-general who investigates military conduct.
Defence Minister Paul Goldsmith said he had received the resignation.
Goldsmith said in a statement that the situation was an "integrity matter" and he had agreed with Davies that his position was no longer tenable.
"I acknowledge his 42 years of service and his contribution to the New Zealand Defence Force, but note the circumstances of his resignation will be a great disappointment to the men and women of the Defence Force," Goldsmith said.
Davies graduated from the US Air Force Air Command and Staff Course at Maxwell Air Force Base in Alabama in 2000, and the Royal College of Defence Studies in London in 2013, according to the New Zealand military's website.
He was appointed a Member of the New Zealand Order of Merit in 1998 for his role in the midwinter evacuation of a critically ill US citizen from Antarctica.
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