The 46-year-old replaces Andy Moles, who stepped down last October amid player appeals for his dismissal.
Captain Daniel Vettori, who acted as coach in last month's series against Pakistan and in preparation for the Bangladesh tour starting next week, also retains a high-level role, New Zealand Cricket (NZC) said.
"We have put a great deal of thought, and consulted widely, about how we progress the current Black Caps unit without upsetting the current leadership momentum within the team," NZC chief executive Justin Vaughan said.
Vaughan said they had "considered the credentials of a number of high-profile international options". Greatbatch, who played 41 Tests for New Zealand, will also continue his role as a Black Caps selector and Vettori will continue his involvement in team selection, tactics and strategy.
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