The former England all-rounder had been in the role for a little under a year, initially on an interim basis as Shane Bond's replacement, before taking it on full-time.
The constant travel away from his young family had been the main reason behind his decision to give up the post, the former Otago coach said.
"At first I thought I could balance the responsibilities but I no longer think that's feasible. I need to be closer to my family," the 38-year-old said in a New Zealand Cricket statement
"I had an amazing time with the team. It's probably been the best time I've had in cricket, either as a player or as a coach."
Australia skipper Steve Smith's side depart for their short tour of New Zealand on Saturday, for an itinerary that begins with the first of three one-day internationals next Wednesday.
The sides also play two tests, the first in Wellington from Feb. 12-16 and the second in Christchurch from Feb. 20.
New Zealand's next international commitment after that series will be the World Twenty20 tournament in India in March.
(Reporting by Greg Stutchbury in Melbourne; Editing by John O'Brien)
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