The fibre optic network will be installed in the city's wastewater pipe network from next year.
It's expected that about 15,000 homes per month would receive access to the network once the rollout begins.
Comment is being sought from Communications Minister Stephen Conroy and the opposition's communications spokesman, Malcolm Turnbull.
The deal with Brisbane-based multinational i3 Asia Pacific would provide homes and businesses access to 100 megabits-per-second broadband, the same speeds the federal Labor government plans to offer on its broadband network.
i3 would act as a wholesaler, providing broadband capability to existing telecommunication retailers, such as Telstra and Optus.
Newman said i3 Asia Pacific was rolling out a similar scheme for the whole of Scotland and had successfully operated similar schemes in the United Kingdom since 2002.
"The NBN program has no firm timetable for a rollout across Brisbane,” he said.
"[It] has not put the needs of Brisbane on as high a priority as we would like and we didn't want local residents and businesses to be left behind in the 20th century.”
The project followed a successful trial and would come at no cost to ratepayers, the mayor said.
“This is a voluntary scheme, there will be no opt-out deals or compulsion to force people onto this scheme,” Newman said.