She said the Anglican Diocese was "delighted to offer a sacred place in Cathedral Square where the whole city may gather''.
The Great Christchurch Buildings Trust, led by former MP Jim Anderton, is continuing to oppose the demolition. It has filed an appeal in the Supreme Court, which is yet to hear the latest arguments in the case.
Mr Anderton said he was not surprised by the church's decision.
"The church, and particularly the bishop, has had its mind set on destroying the cathedral from the very beginning. We've known that, and the so-called consultation was a sham, really.''
He said the church was not bothered by the trust's latest appeal.
"They've just gone ahead and decided to build a new one without the Supreme Court even hearing the case. It's ridiculous, really - unless you look at the history of this and then you realise, as far as the church is concerned, it's been a done deal all along.''
Restore Christchurch Cathedral campaign co-ordinator Mark Belton said there was every indication the bishop had been determined to reach the outcome.
"We remain resolute, because it's an absolute no-brainer, that the cathedral should be restored for the benefit of Christchurch.''
Mr Belton said the church had demonstrated it was not fit to be a custodian of the building and it should step aside.
"It should be passed to representatives of the city, community and New Zealand who care about extremely important heritage buildings of this nature.''
Mr Belton said it was regrettable the matter had gone to court, but he was hoping for a successful outcome.
"We are hopeful that the appeal to the Supreme Court will be accepted and that the submissions, that would require the church to become a responsible custodian of the building and restore it, will win the day.
"If they don't, sadly it will carry on because there will be more court actions outside that one.''
