Greatbatch will stay on as the side's batting coach and has also been appointed as chairman of the Black Caps' selection panel.
An under-strength India side thrashed the Kiwis 5-0 in a one-day series earlier this month, extending the tourists' losing streak in one-day matches to 11 with the World Cup on the sub-continent just two months away.
The Black Caps are on a wretched run of form and suffered a 4-0 defeat in a one-day series to Bangladesh in October before losing a three-test series against India 1-0.
"A thorough review of the Black Caps tour of India has been undertaken over the last week," NZC chief executive Justin Vaughan said in a statement.
"The changes being made are a direct result of that process and should make a real difference." Former test captain Wright, 56, who had a successful coaching stint with the India from 2000-05, is to take charge immediately with the Dec. 26 Twenty20 match against Pakistan as his first assignment.
The new selection panel would be made up of Greatbatch, Glen Turner and Lance Cairns, NZC said.
New Zealand will host Pakistan for three Twenty20 matches, two tests and six one-day internationals before heading to the World Cup, which begins on Feb. 19.
