Ms Wade-Brown said the city had the lowest rate of smokers in the country.
"Already less than 10 per cent of Wellingtonians smoke - the lowest rate in New Zealand.
"We can become the first smoke-free capital in the world by helping 5000 of our fellow Wellingtonians to become smoke-free over the next nine years," she said.
Community, sport and recreation committee chairman Paul Eagle supported the smoke-free extension.
"We need to take this seriously as the capital city and ensure we do everything we can to make Wellington smoke-free by 2025.
"It's not just the smokers' lives that are of concern; smoking has a huge impact on wider communities and especially that of Maori and Pacific communities, where smoking rates are still as high as 33 per cent," he said.
Observational surveys revealed the vast majority of smokers were respecting smoke-free areas and didn't smoke around children.
Smoking in some downtown areas has been observed at 13 per cent or more, but drops below 3 per cent when children are around
Little or no smoking was observed at sports grounds when kids were playing.
Wellington's playgrounds and sports parks went smoke-free in 2012.
Wellington City councillors also agreed to look at the possibility of a by-law against the littering of cigarette butts.
In 2011, the Government set a goal for New Zealand to be smoke-free by 2025, meaning a smoking rate of less than 5 per cent across all populations.