It was also announced in Auckland today that an independent selection panel would be created and will exclude the coach and captain, Daniel Vettori.
Greatbatch will chair the selection panel, which also includes former New Zealand cricket greats Glenn Turner and Lance Cairns.
Turner retains his role as a selector but Cairns, who is currently a selector for the New Zealand under-19 team, is new to the setup.
The coach and captain will continue to contribute to the selection process and will be actively responsible for team selections on tour, but they will not be on the selection panel, as was the case under the previous regime.
That leaves Vettori to concentrate on captaining the team, a change critics have long been calling for.
Greatbatch, who took over from Andy Moles after the Englishman was forced to quit in October last year after a senior player revolt, will continue his role as batting coach within the New Zealand Cricket (NZC) high performance programme.
NZC chief executive Justin Vaughan said the restructuring was a result of a review of the India tour, the win-loss ration of which had not been acceptable.
New Zealand have lost 11 consecutive one-day internationals. They were defeated 5-0 in India earlier this month, 0-4 by Bangladesh in the subcontinent in October and lost their last two matches in a tri-series in Sri Lanka in August.
The one-day World Cup is being held in the subcontinent in February-March next year and New Zealand's form has been deemed dire enough to warrant significant changes to the management setup.
While he was positive about the changes, Vaughan said they would not be a panacea.
"Structural change and coaching change will not immediately turn this team around; that will take dedicated hard work, persistence and a bit of patience. But it is, I believe, giving the team its best possible chance of success for the Pakistan tour and for the World Cup."
Vettori had wanted Wright to be involved with the team for some time and was supportive of the changes, Vaughan said.
Wright said he was very excited to be given the job, but acknowledged it would be a great challenge to coach the team to winning form.
"I look at, particularly the one day team, and if it plays to its potential it's a very, very good side, and that excites me actually. But the trick is to help the players find that consistency and help them to rediscover that form, that confidence."
The coaching support staff would also be stripped-back as part of the restructure, which suited Wright.
"I like close, tight teams -- I've always felt that everyone has to be busy and active. You don't want to get in the way of players, it's really important that players have space and can simplify and concentrate on what they have to do, which is playing. I've always favoured less rather than more."
The coaching support staff for the upcoming Pakistan tour would be announced this week, and Wright said he had an idea of the sort of people he wanted to work with.
"I have a few faults myself and I think one of the big tricks is putting the right people around you so you work together and you use each other's strengths."
Wright, 56, a former New Zealand captain, enjoyed success as coach of the Indian cricket team between 2000-05 and is credited with laying the foundations for India's current success during his time with the subcontinental powerhouse.
During his time as coach, he led India to a 2-1 home test series win over Australia, a test series win over Pakistan and to the final of the 2003 World Cup. He was replaced in May 2005 by Australian Greg Chappell.
Wright, who played 82 tests and 149 one-day internationals as an opening batsman for New Zealand between 1978 and 1993, will take over the coaching reins immediately, starting with the series-opening Twenty20 international against Pakistan at Auckland on Sunday.
His contract is until the end of the team's tour to the West Indies in mid-2012.
