The US will not have to say whether the ship is nuclear powered or armed.
Under New Zealand's 1987 anti-nuclear law, Key has to sign a declaration that he is satisfied the ship complies with New Zealand law - and such information is publicly known these days.
Greenpeace NZ was one of the first to claim a victory.
"We stood up to the mightiest military power on earth, not to mention a traditional ally, and we won," said executive director and ex-Green Party leader Russel Norman. "Regardless of what you think of the US Navy, or other navies, this is an historic victory for people power."
Peace activist and author Nicky Hager said the visit would be a clear victory for New Zealand's nuclear-free stance.
"There has been a lot of pressure for New Zealand to be the one to back down," Hager said. "And it's kind of a miracle that New Zealand stuck to its policy through all these years and now with an American ship coming here on our terms."
Labour deputy leader Annette King described the announcement as a "red letter day" for New Zealand's non-nuclear status and saw it as an acceptance by the US of New Zealand's nuclear-free policy.
"I would characterise it as a victory for the relationship between New Zealand and the United States," Key said.
"It is not a victory for one side or a defeat for the other. It is a sense that actually our relationship is more important. We have dealt with the matter. It is somewhat historic now and we are taking the next step forward."
ABs, Clark - Biden digs it all
Joe Biden moves from humour to formality like a slalom skier.
He says John Key was so strong in his support of his former opponent Helen Clark for next UN Secretary-General, he thought she was his sister.
But seriously, the US was impressed with her too, and she was one candidate it was closely considering.
The Vice President talked about getting an All Black jersey from Jerome Kaino and Charlie Faumuina yesterday which puts him in mind of his love of the game which he played "400 years ago" and a trip to Ireland - his mother was Irish - with his brother to see the All Blacks play.
"It was nothing but carnage left behind."
He was honoured to receive a traditional Maori welcome for himself and his three granddaughters.
"Kia ora and by the way I am not going home," were his opening words of his press conference. "What a beautiful, beautiful, beautiful country and a beautiful city."
"I doubt any of you who have visited the United States have ever, ever received anything other than a warm welcome," he said. "There is a real, genuine affection for New Zealand in the United States. My only hope is that there is a significant affection for the United States here."
