Legislation was due to be passed around the middle of next year, Davis said.
He said the levy was one part of a package of initiatives designed to make sure the tourism industry is sustainable, productive and inclusive.
The levy will give New Zealand the opportunity to be a "world leader in destination management".
Conservation Minister Eugenie Sage said public consultation showed the levy had strong support, adding that 107 submitters were in favour of setting the fee at $35.
"The money raised through the levy will help improve the protection and enhancement of New Zealand's distinctive natural environment and improve tourism planning," she said.
"The chance to enjoy Aotearoa's spectacular landscapes and nature are a major reason international visitors come to our country."
National's Tourism spokesman Todd McClay said the tax was unnecessary.
"According to Deloitte, the Government already collects $3.27 billion a year in international tourism-related revenue and spends $638 million on the industry, receiving a net gain of more than $2.6 billion."
McLay said if the Government continued to add more costs such as these "we'll see fewer people choosing to travel here".
Earlier this year, Davis had suggested the tax would be between $25-$35 per visitor.
But Cabinet has settled on the $35 fee.
In July, he noted some of the concerns of the tourism industry and the airline industry but said the levy would not add major delays at the airport.
"We don't believe the financial burden should rest solely on the shoulder of New Zealanders, we do believe visitors should pay their fair share."
Davis said the intention is for funds to be split evenly between conservation and tourism.
He said further work with stakeholders would now be done to decide the best ways to spend the levy's revenue.
"We have a couple of options on how to do this and will work through those with our partners, but the main feature of the levy is that its revenue will be set aside for conservation work and tourism infrastructure."
