The conditions have been met.
The offer, which was approved by the Anglican synod in September, also included a $10m grant and $15m loan from the Government, and $13.7m from the Great Christchurch Buildings Trust rebuild campaigners.
The city council is planning to ask for public views on the $10m grant.
The church would contribute $42m from the cathedral insurance proceeds.
A fundraising campaign aims to make up the rest of the estimated $104m cost.
The rebuild and restoration work is expected to take seven to 10 years.
The city council will also decide tomorrow how to run the public consultation process.
The current proposal is to seekwritten submissions between October 12 and November 13.
People could then make verbal submissions at a hearing in either late November or early December and councillors would then make a decision before the end of the year, said mayor Lianne Dalziel.
She said she had felt an "overwhelming sense of relief" when she heard the decision had been made to reinstate the cathedral.
"We were New Zealand's first city established by Royal Charter 31 July 1856. This required a commitment to build a cathedral - a seat for the bishop. So the historical connection with the cathedral is very real," she said.
But since the 2011 earthquake, it was clear people were divided about whether to repair or build a new cathedal.
"But we were united in wanting a decision, because the lack of a decision was holding the city back."
She said consultation would give people a chance to play a part in that process.
