Dean Kelly-Moore says the new look will complement the old.
The chapel is designed to fit into the south end of the cathedral, which has been built in stages since 1959.
The canopy will come from beneath the cathedral's rose window, that looks over a memorial garden towards One Tree Hill.
The chapel will be close to the east wall of the historic wooden St Mary's in Holy Trinity, the old cathedral, which which was moved on to the cathedral site from across the road 30 years ago on Thursday.
The dean said St Mary's was a "working church, a busy place" and as part of the works, would be integrated with the chapel and get a formal link to the cathedral.
Cathedrals took generations to build and the chapel project would be 'this generation's contribution to the cathedral".
She hoped the work could be finished in time for the bicentenary of Christianity in Aotearoa New Zealand on Christmas Day 2014.
About half of the $10 million budget is for refurbishing the cathedral's organ.