The former New Zealand representative will take up the appointment ahead of the series against the touring Bangladesh side, which begins with a Twenty20 match in Hamilton on Wednesday.
New Zealand Cricket said Greatbatch, a left-handed batsman in his playing days, would join the existing coaching team of Mark O'Donnell and Shane Jurgensen.
He would take on particular responsibility for developing batting performance within the team.
NZC chief executive Justin Vaughan said skipper Daniel Vettori would continue his high-level involvement in team selection, tactics and strategy.
Vaughan said there had been a lot of thought on how to take the Black Caps forward, without upsetting the momentum established by the current leadership.
"I know Mark is strongly supportive of the way the team has progressed and will complement Daniel well."
Greatbatch replaces Andy Moles, who resigned in October after players expressed dissatisfaction with his methods.
Vaughan said NZC considered several high-profile overseas options for the job.
Greatbatch was highly respected in cricketing circles both in New Zealand and internationally, he said.
"Mark is already close to the team by virtue of his selectorial role, and through his recent stint with the team in Dubai," he said, referring to the Blackcaps' series against Pakistan.
"Our experiences with Mark have been consistently good. His recent elevation onto the national selection panel has been viewed as an outstanding success, and he has received overwhelming praise for his communication and honesty with players and coaches."
Greatbatch (46) said he was looking forward to working even more closely with the squad and was excited by the potential there.
"There is a real desire for success within this current Blackcaps unit and there are some very talented individuals," he said.
"I believe that I can make a very positive contribution to the team and to the batting unit in particular."
