"New Zealand Cricket today announced that John Wright will assume the position of Blackcaps head coach, effective immediately," New Zealand Cricket said in a statement.
The decision was one of several changes in the team management after a review of the recent tour to India in which the Kiwis lost the Test series 0-1 and were whitewashed 0-5 in the ODIs.
The thrashing followed an embarrassing 0-4 loss to Bangladesh in an October ODI series.
Wright, who played 82 Test and 149 ODIs, coached India from 2000 to 2005 before joining NZC to oversee its High Performance programme.
The 56-year-old will assume responsibility immediately, with his opening match being the Boxing Day Twenty20 International against Pakistan.
Besides appointing Wright as coach, the NZC also appointed an independent selection panel with Greatbatch as its convener.
"Greatbatch will also continue his role as batting coach within the New Zealand Cricket high performance programme," the NZC said.The panel will also have Glen Turner and former international Lance Cairns, who is currently a selector for the New Zealand Under-19 team.
"The coach and captain of the national team will continue to contribute to the selection process and will be actively responsible for team selections on tour," the NZC said.
NZC CEO Justin Vaughan said all the changes have been agreed upon unanimously.
"All aspects of the tour-playing performance, preparation, selection and support staff - were examined to ensure that the Blackcaps have the greatest chance of succeeding.
"The changes being made are a direct result of that process and should make a real difference," said Vaughan.