"We are keen to fill this critical role as soon as possible but are conscious that we need to take the time to find the right candidate who can take us through to the 2015 ICC Cricket World Cup.''
Wright was held in high regard by his players, but said the travel grind of international coaching had become tiresome following his stint coaching India from 2000-2005.
Last September, New Zealand Cricket introduced a controversial selection set-up under the watch of former Australia supremo John Buchanan who joined NZC as the director of cricket.
Buchanan dis-established the existing selection panel and installed fellow Australian Kim Littlejohn as the national selection manager.
Littlejohn was given the power to pick the national teams in conjunction with the six domestic coaches with a final sign-off from Wright.
That system appeared to be at odds with Wright's style and could have been an underlying reason for his departure.
New Zealand have a heavy diet of cricket over the next 14 months with away test matches against West Indies, Sri Lanka, India, South Africa and England.
They will contest the Twenty20 World Cup in Sri Lanka in September and also host the English side in February and March.
Wright was finally appointed as head coach of New Zealand in December 2010, following a drawn-out process and months of limbo for the national team, during which the team appeared to be coached by captain Daniel Vettori.
The set-up was a shambles after Andy Moles resigned in October of 2009 amid claims he had lost the respect of his players. Mark Greatbatch was installed as coach early in 2010 but often referred to himself as the "batting coach'', while Vettori had a major say in team tactics.
When Wright stepped in, Greatbatch was officially named batting coach and joined a three-man selection panel with Glenn Turner and Lance Cairns.
They were relieved of their duties when Littlejohn came on board.
Wright took New Zealand to the semifinals of the 50-over World Cup in the sub-continent last year.
He later orchestrated one of the most memorable test victories in New Zealand cricket history when Doug Bracewell bowled the Kiwis to a seven-run win over Australia in Hobart in December, levelling the series 1-1.
Next up were South Africa, who proved a tougher challenge beating the Black Caps in their Twenty20, one-day and test series during the summer.
During Wright's tenure he promoted the likes of Bracewell, Trent Boult, Tom Latham and Ronnie Hira to international cricket and turned BJ Watling from a test opener into a wicketkeeper-batsman.
Record under Wright:
Tests - Played 9: Won 3, Drew 3, Lost 3
ODIS - Played 23: Won 12, Lost 10, 1 no result
T20s - Played 10: Won 7, Lost 3
From the archive:
Dec 2010 - Black Caps enter the age of Wright
Dec 2010 - Wright must teach how to play with grit