New Zealand Football CEO Andy Martin said Hudson, who is signed through until the end of the 2018 FIFA World Cup campaign, shone out from over 100 applicants for the role.
"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," 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 side and ninth Englishman. Neil Emblen had been the interim coach since Herbert left the role.
Hudsonsaid he can't wait to get started working with the All Whites as the journey towards Russia begins.
"I'm 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."
After resigning from his position with Bahrain last week, Hudson has relocated to New Zealand for the fulltime role which also includes responsibilities in overseeing the programme of the country's age-group representative sides.
The first test for Hudson and the All Whites team will come in September's away clash with Uzbekistan.
Anthony Hudson
Age: 33
Qualifications: UEFA Pro License, UEFA 'A' License
Coaching experience:
2013 - Bahrain senior national team coach
2012-2013: Bahrain U-23/Olympic Games national team coach
2011: Newport Country FC manager (Football League, UK)
2010-2011: Tottenham Hotspur FC reserve team coach
