Prime Minister John Key announced on Wednesday the government was backing the $2.68-billion project and says construction is likely to start in 2020.
He's denying the government has backed down and says the project was never ruled out craft organizers
The link was first proposed in 2011, and until now the government hasn't been enthusiastic about it.
Auckland City Council wanted it up and running by 2020 but Mr Key says the government's timescale is a bit slower than that.
Mr Brown says a lot of the preliminary work has already been done and he's going to talk to the government about "the exact timing" of the project.
"It will double the capacity of the existing rail network and slash travel times," he said.
"Travel times from the west and the south will be slashed by up to half an hour."
Mr Brown says the economic benefits can't be understated.
"Auckland's city centre population is expected to double by 2041. This will lead to gains in productivity that will more than double the city centre's economy."
Mr Key confirmed the government would pay part of the cost, but wouldn't say how much.
He will announce details in a speech on Friday.
"Auckland will have to find ways to meet its contribution."
Mr Key isn't ruling out a public-private partnership to build the link and says there are a number of options.
The government's share will be through a one-off appropriation.
Labour and the Greens say it's a major U-turn by the government.
"They've been bagging the rail link for years and years, they hate it," said Labour's transport spokesman Phil Twyford.
"This makes John Key and (transport minister) Gerry Brownlee look really stupid."
The Greens are claiming victory, saying they've always backed the rail link.