The company said the move was part of a plan to expand its production space and consolidate its footprint in the UK.
Amazon Studios spent $465m (£336.5m) on the first season of the show.
With four more seasons expected to be made, that would make it one of the most expensive series in television history.
New Zealand's dramatic landscapes were also home to Oscar-winning director Peter Jackson's The Lord of the Rings and The Hobbit movie trilogies.
Amazon said work on season one of the show would be completed in the country before production shifts to Britain.
In a statement announcing the decision, Vernon Sanders, vice president and co-head of TV at Amazon Studios thanked "the people and the government of New Zealand for their hospitality and dedication and for providing The Lord of the Rings series with an incredible place to begin this epic journey."
New Zealand's economic development minister Stuart Nash said he was disappointed by the decision.
"I am enormously proud of the New Zealand screen sector. The Amazon Studios' decision in no way reflects the capabilities of our local film industry or the talents of the people who work in it," Mr Nash added.
Season one of the show is scheduled to make its worldwide debut on Amazon's Prime Video on 22 September next year.
The move is set to be a major boost to the UK's film and television production industry as it brings hundreds of millions of dollars into the country.
The UK's Department for Digital, Culture, Media and Sport did not immediately respond to a BBC request for comment.