Almost a year after the Kaikōura earthquake caused the partial collapse of two floors in Statistics House, insurers have finally agreed the building should be demolished.

Derek Nind, chief executive of CentrePort, which owns the building, said an agreement had been reached that the six-story office building could not be economically repaired.

"We've had our engineers do their reports and the insurance companies have had theirs do theirs and the insurance companies has come to this conclusion," Nind said, describing damage to the structure as "substantial".

KEVIN STENT/STUFF Damage to Statistics House could be seen from outside the building in the days following the earthquake.

CentrePort's shareholders - the Greater Wellington and Horizon regional councils - had been notified and the company would apply to Wellington City Council for consents to demolish the building.

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Previously home to hundreds of employees of Statistics NZ and the Ministry of Transport, the failure of Statistics House became one of the focal points of the November 14 earthquake.

While "critical issues" were identified with its design in 2013 following the Seddon earthquake, staff continued to work in the building. Strengthening work was underway at the time of the November earthquake.

Government Statistician Liz MacPherson, the chief executive of Statistics New Zealand, welcomed the news, which would allow the organisation to "draw a line under our past connection with Statistics House".

"We will be forever thankful that the quake happened just after midnight last November when nobody was in the building, rather than at midday during the work week," MacPherson said, echoing a post to staff she delivered shortly after the earthquake hit.

Although an agreement has been reached to demolish Statistics House, the future for the site is unclear.

Nind confirmed it had "full replacement insurance" for Statistics House. That could oblige CentrePort to replace the building.

Nind said the agreement with the insurance was simply about demolition. "There's been no decision made about what we're going to do next."

Statistics House was part of a major venture by CentrePort to expand into commercial property, which also saw it build Customs House and BNZ Harbour Quays.

All three buildings have been empty since the earthquake, although repairs are underway on the Customs building, which could be reoccupied before the end of the year.

Experts were still assessing the BNZ building, and Nind did not know when the future of the building would become clear.

Wellington Mayor Justin Lester welcomed the news about Statistics House, saying while it was hardly a surprise, it provided certainty and potentially freed up land for another use.

"I'm looking forward to sitting down for a chat with CentrePort and the Greater Wellington Regional Council about the best possible use for waterfront land, and those discussions are still to take place, but I think it's fair to say we're on the same page," Lester said.

"We all agree we've got an opportunity, we've got some land that could be freed up."