"The public now has a chance to have its say on which design best reflects that shared loss and experience."
The memorial will "honour the victims of Canterbury's earthquakes and acknowledge the suffering of all those who lived through them, as well as the heroism of those who participated in the rescue and recovery operations", Ms Wagner said.
Christchurch Mayor Lianne Dalziel said it was an important step towards having a memorial space for locals and visitors to share.
"Allowing the public to have a say in how we commemorate what we have lost, while capturing a sense of hope for the future, will make a real difference," she said.
Te Runanga o Ngai Tahu director Sir Mark Solomon said: "It is very important for the region, our city and our communities to have an appropriate place to honour and reflect on the events of the earthquakes. I believe as a community we will achieve this."
The designs can be viewed online, and will also be on display at Christchurch Botanic Gardens on the walkway alongside the Canterbury Museum between February 24 and March 15. Public feedback will be received until March 15.
Following the public consultation period, stakeholders -- including emergency service first responders and victims' families -- and a panel of arts professionals and architecture experts will recommend a preferred design to the memorial leadership group, made up of Ms Wagner, Ms Dalziel, Sir Mark and Minister for Arts, Culture and Heritage Maggie Barry.
The final decision rests with Minister for Canterbury Earthquake Recovery Gerry Brownlee.
The Government has set aside up to $10 million for the memorial, along with $1 million from the Christchurch Earthquake Mayoral Relief Fund.
It is hoped the memorial would be completed in 2016.
This Sunday will be the fourth anniversary of the deadly February 22 quake.
More information on the short-listed designs can be found here.
