The 33-year-old, who left his position as Bahrain's coach last week, succeeds Ricki Herbert, whose eight years in charge ended with a 9-3 aggregate loss to Mexico in a two-legged playoff for a 2014 World Cup finals place.
Hudson promised his side would entertain the fans.
"They can expect to see a team that goes out to try and win games," he told reporters. "They can expect to see a team that is organised but with a real positive attitude, a team that plays football and tries to win the ball high up the pitch.
"Our team will have a real emphasis on being positive going forward and makes the most of the qualities of the players available for selection."
Hudson was born in the United States when his father, former England midfielder Alan, was playing for the Seattle Sounders. He has been described as a "young Jose Mourinho" by Harry Redknapp after working under the now Queens Park Rangers boss at Tottenham.
Unlike neighbours Australia, who moved to the Asian Football Confederation in 2006, New Zealand have stuck with the Oceania region, which offers easier opponents but no automatic berths for the World Cup finals.
"A big pull of why I've come here is to go to the World Cup. And not just go to the World Cup but go further than we've ever gone," the coach added. "Along the way to reaching that target, I'm very passionate about playing the game a certain way.
"I want that style of play and that philosophy to be embedded in what we do through the younger age groups and for it to be a style of play that the people of New Zealand are proud of and excited to watch."
Hudson got his first head coaching job at senior level in 2011 with Welsh non-league club Newport County, where he lasted just five months before being sacked.
He moved to Bahrain to work with the under-23 side under fellow-Englishman Peter Taylor in 2012 and led the team to the title at the 2013 Gulf Cup of Nations.
After taking over the senior team in August 2013 he helped them qualify for the Asian Cup as group winners and signed a new contract through to 2016 earlier this year.
The Gulf state's football association have already said they would challenge his exit through the courts.
Hudson's first test as New Zealand coach will be September's clash against Uzbekistan in Tashkent.
(Reporting by Sudipto Ganguly; editing by Peter Rutherford)
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