"I've been astonished, in the interactions I've had, about how excited Kiwis are to bring the birds back."
The project will cost $15 million over the 10 years, and is based on suburban backyard trapping groups setting up the traps in their own areas.
In return, it is hoped those people will quickly see native birds flourish in their backyards.
Fenwick said it would create an "army" of thousands of volunteers.
"Thousands of people, out there at the weekends, setting their trap lines, planting trees, doing this wonderful work in their community.
"Of all the proposals we've seen, Wellington is the strongest in terms of the community at work."
Mayor Justin Lester said it was amazing to see once-rare birds becoming common in urban centres.
"There is only one glaring disappointment, in Johnsonville. Lots of traps, and I'm yet to catch a rat.
"I apologise, and will keep working hard. Hopefully that's due to reduced numbers, but it could be due to my catching ability."
Goodnature traps will be used to help get the capital pest free.
Co-founder and design director Robbie van Dam said the project had the type of ambition that would make New Zealand a leader in conservation.
"This initiative will help us to protect our national symbol and revive it to healthy numbers.
"I look forward to seeing those kiwi road signs installed in Brooklyn.
"It has been an ambition of ours for nearly a decade to see Kaiwharawhara act as a boundary that fences off the lower North Island so we can make Wellington a predator free city.
"As a Wellington bred and based company, we're really excited to see our beautiful home become the first predator free capital in the world."
The Miramar Peninsula will be the first focus area for the project, as it is the most easy to defend from predator reinvasion.
The total area will be 30,000ha of urban and rural land, with an estimated 70,000 households within its boundary.
Taranaki has previously announced its plan to become the first predator-free region in New Zealand.
