Speaking at a press conference on the future of the 120-year-old cathedral today, Bishop Matthews revealed that demolition work will begin before Christmas.
She said: "The decision has been made to make the cathedral, which is severely broken and has gone through a very rough time, safe.
"To do that requires some partial demolition, and full demolition, and we're going to do that so we can get what is important out - our heritage.
"That means the future of the cathedral, which is important to all of us and so symbolic, will involve a mixture of old and new, with a view of returning to being the heart of the city and the heart of the diocese, and a place greatly loved by all.''
The bishop added: "One thing we are not doing - the least desirable option - is to bring the whole thing down and to put the whole thing up again, because no-one wants that. It will not be a replica.''
The cathedral withstood violent earthquakes in 1881, 1888, 1922, 1901 and on September 4 last year.
But the 6.3-magnitude earthquake in February, which reduced the cathedral's spire to rubble, was followed by further significant damage on June 13.
The extent of the damage makes the building unpredictable and therefore unsafe.
Reverend Peter Beck, dean of the cathedral, said today's decision gives the church time to "explore further options''.
He said: "It helps us work together to build the most amazing, wonderful building which will respect our heritage and build for the future.''
Mr Beck also confirmed the church is looking at building a transitional "cardboard cathedral''.
He added: "It's our prime option at the moment.''
The cathedral will be deconsecrated at a service on November 9, which will return the building to secular use.
New Zealand Historic Places Trust Board (NZHPT) welcomed today's announcement.
Chief executive Bruce Chapman said: "Along with other members of the collaborative group including engineers who had examined the cathedral, we agreed that the preferred option was making the building safe and retaining as much of the building's heritage fabric as possible.
"While there is much work to be done and some uncertainty remains, today's decision will be welcome news for everyone who has lived in Christchurch, worshipped in or visited the cathedral.
"It is an iconic heritage landmark regionally, nationally and internationally - reflected in its current Category I registration with the NZHPT.''
The cathedral was consecrated on November 1, 1881.
It was designed by English Gothic designer George Gilbert Scott, but influential local architect Benjamin Mountfort supervised the work.
Although the building is based on traditional European cathedrals, it contains a number of New Zealand influences, including the use of matai and totara timber from Banks Peninsula, and stone came from local quarries.
Artwork on the walls express the Maori, Polynesian and European culture, with New Zealand flora and fauna depicted in stained glass and in carvings.