Mr Copeman said all but four of the 92 shops had been leased, and the tenants were happy they could run a business in Queen St "for as little as $300 a week".
Businesses running from shops sized from 12sq m offer products and services ranging from Maori souvenirs, Asian groceries and washing machines to beauty and massage therapy treatments.
Within the next couple of weeks, a second level comprising an indoor sport and entertainment centre and an international food court will also open there.
Auckland Council business advisory chairman Cameron Brewer says "little shoebox shops selling absolute rubbish" contradict the mayor's vision of "creating a world-class city centre".
It was also suggested some stores were being operated for immigration purposes, allowing migrants to establish businesses to gain residencies.
But Fountain Youth beauty spa owner Anita Yu, 28, said there was no truth in the allegation and that most operators, including herself, signed up for tenancies because of the market's location and cost.
"We have been looking at having a Queen St presence for quite a while now, and this market has made it possible because of the lower rent," said Miss Yu, who also co-owns Gold Coast Health Spa in Victoria St.
"Our clients, who are mainly Chinese international students, are happy with this set-up and we are happy, too, because we can offer them our services at competitive rates." Marie Cotter, who owns and operates Tarati Design, a Maori arts and crafts stall, said affordability was also why she decided to set up shop at the market.
Chinese student Stacey Gui, 21, who lives in an apartment in Hobson St, said she was thrilled at the development.
"Living in the city centre in Auckland is really boring, and I think this market will help bring some life into the city."
A powhiri and cultural performance will officially open the market on June 29.