The 33-year-old was widely tipped to get the job after he quit as coach of the Bahrain national team at the weekend.
Hudson, the son of former England midfielder Alan Hudson, takes over from Ricki Herbert who stepped down last November after a disappointing World Cup qualifying campaign.
More than 100 applications were received by New Zealand Football for the head coaching role with Hudson making it to a short-list that also included Australians Frank Farina and Gary van Egmond.
“We have a clear vision for the All Whites moving towards the 2018 Fifa World Cup in Russia and we believe Anthony is the candidate best suited to the task of bringing that vision to life,” NZF chief executive Andy Martin said.
“He is driven and has achieved a lot in coaching terms at a relatively young age and given the make-up of our side, we believe he is an excellent fit for our environment.”
Hudson is the 16th coach of the New Zealand national men’s team and has signed until the end of the 2018 World Cup campaign.
“I am excited to be joining New Zealand Football as the next coach of the All Whites,” Hudson said.
“With the playing group energised by some exciting young talent in recent times, the All Whites role is an attractive one and I intend to build a programme for New Zealand’s top players which gives them the chance to show the world what they can do.
“It’s an exciting prospect for everyone involved and I’m looking forward to the challenges ahead in what is the next chapter of a developing football story in New Zealand.”
Hudson will have only a few weeks to get to know his new players as the All Whites are due to head to Tashkent on September 8 for a friendly international against Uzbekistan.
Neil Emblen, who was interim head coach for the All Whites’ matches against Japan and South Africa earlier this year, will stay on as Hudson’s assistant for the Tashkent game and will select the squad.
Hudson, who has been described as a “young Jose Mourinho” by Harry Redknapp, had four wins, five draws and three losses, during his year in charge of Bahrain.
The ambitious former Newport County manager and Tottenham reserve coach is the youngest coach to get his UEFA Pro Licence.