Hudson has signed a deal through to the end of the 2018 World Cup after Herbert retired in November following New Zealand's failure to qualify for the finals in Brazil.
The 33-year-old Englishman arrives from Bahrain, where he gained promotion from the under-23 squad to the senior side in August last year, helping the nation book their place at the upcoming Asian Cup in Australia.
Hudson held off competition from former Australia coach Frank Farina and Gary van Egmond to secure the role and he will kick off his tenure with an international friendly against Uzbekistan on September 8.
"I'm excited to be joining New Zealand Football as the next coach of the All Whites," said Hudson.
"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 is tasked with adding to New Zealand's sole World Cup appearance in 2010 with qualification for Russia in four years time, an assignment he is relishing.
"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," he said.
"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."
