The embattled city's most celebrated landmark building will be "deconstructed" to a "safe" level of 2m-3m and will not be rebuilt.
The news was met with dismay in Christchurch.
The cathedral has been extensively damaged in earthquakes over the past 18 months. Its spire snapped in half during the fatal 6.3-magnitude quake of February 22, 2011.
Ongoing shakes have caused further damage.
Bishop Victoria Matthews, of the Anglican Diocese of Christchurch, said: "The cathedral will be deconstructed with the utmost care and respect, while at the same time protecting the treasures within its walls. There will be no bulldozers or wrecking balls on the job."
The safety measures will allow the retrieval of taonga and heritage items.
The Rt Rev Matthews said a rebuild was not feasible, nor was a replica cathedral, saying it would cost more than $100 million.
"We would not be responsible stewards if we ignored the financial realities," she said.
"The Anglican Diocese is facing a hard reality. The cathedral is the revered `Mother Church' but is not the only church in the diocese to have sustained damage, in some cases irreparable or too costly to repair."
She could not rule out a full demolition, admitting: "It is in the realms of possibility, but it is not desirable."
The church said the deconstruction would likely be completed by the end of the year.
A new "beautiful, inspiring, safe" cathedral would be built somewhere, but it would take "years, not months".
"We acknowledge the high level of community interest and sense of ownership as the cathedral was both an iconic building and a place of regular worship by many. However, this is now a very dangerous building that needs to be made safe."
The 131-year-old cathedral withstood violent earthquakes in 1881, 1888, 1922, 1901 and even September 4, 2010.
Christchurch Mayor Bob Parker said the news would be "heartbreaking" for many people in Christchurch.
Heritage campaigner Neil Roberts, of the Christchurch Civic Trust, was critical of the church's decision, arguing more time should have been taken to consider other options.
"Engineers from overseas who are experienced in earthquake strengthening have said `Of course we can save parts of this building'. We don't have to deconstruct it or pull it right down. But they are not listening to that."
The Wizard of Christchurch described the decision as "an unforgivable act of barbarism".
Ian Brackenbury Channell (79) has performed in front of the central city landmark building in Cathedral Square for decades.
He has started a petition against the demolition.
The New Zealand Historic Places Trust also expressed its disappointment, saying the building could have been restored or rebuilt in a recognisable form.
"The church's decision to deconstruct the cathedral down to sill level, or a maximum of 2m-3m around the full extent of the building, will make it very difficult to retain any sense of this very important building as it once was," NZHPT chief executive Bruce Chapman said.
Earthquake Recovery Minister Gerry Brownlee called the decision a "courageous" one.
