The gallery is subject to an amended staged consent process.
Building work is ongoing, but none is in public areas, Mr Jones said.
A certificate of compliance is not expected to be applied for before the end of next month.
The 12-year-old building, which has the phrase "Everything Is Going To Be Alright" emblazoned in colourful letters on its side, became the hub for the civil defence response to the deadly February 22, 2011, earthquake.
Seven months later, the true extent of its damage -- largely beneath ground -- became known and it was shut down for repairs and strengthening work.
In April last year, base isolation work began to bolster its foundations, allowing the building to "float" in any future tremors.
"We can't wait to open our doors to the people of Christchurch on Saturday," gallery director Jenny Harper said.
"Our team has put together an exciting selection of exhibitions, and we want to show our visitors what an exceptional art collection this city has."
Around 360 artworks will be on display in the opening exhibitions upstairs, downstairs, in the foyer and on the roof.
Visitors will be able to view old favourites, including Michael Parekowhai's bronze bull Chapman's Homer, as well as a selection of the 500 new pieces the gallery has acquired over the past five years.
Five new trustees with specialist experience in specific areas have been appointed to the Arts Centre of Christchurch Trust Board. Puamiria Parata-Goodall, Grant Dean, Felicity Price, Mark Todd and Olivia Egerton join incumbents Jen Crawford, Michael Rondel and Erin Victoria Jackson.