Customs Minister Jenny Salesa said the bill, which had all three readings today, closed a loophole that allowed people to smuggle in cigarettes and tobacco and not pay excise tax.
At the moment, Customs have to prove the importation is for the purpose of evading excise tax, before the tobacco can be seized or a prosecution started.
Salesa said the changes meant Customs would be able to take quicker action if the importer doesn't have a permit.
The permits are free and the bill doesn't change duty free allowances or the price of cigarettes.
Seizures of cigarettes increased 352 per cent between 2015 and 2019 - in two weeks in August last year 2086 packages of cigarettes were intercepted in the mail.
The amount of illegal tobacco seized represented a loss of $10.8 million in excise tax.
Salesa said as well as the lost revenue, the smuggling also undermined law and order objectives and the 2025 smokefree goal.
"Given the involvement of organised crime, money laundering, and circumventing the smokefree controls urgent action is required."
The National Party supported the bill and Tim Macindoe, a former Customs Minister himself, said the bill tackled a very serious issue.
"I can be pretty confident that somebody working for [Customs] just in the last hour or so has probably detected illicit tobacco coming in, because it comes in the most bizarre ways, often very crudely disguised in heat pumps and other appliances, in ornaments, and all sorts of bizarre packages," Macindoe said in the House.
But he questioned why it had been treated with urgency as the bill didn't rebuild New Zealand or create jobs.
Act leader David Seymour said the bill would create more bureaucracy without addressing why the tobacco black market existed - the cost of cigarettes.
"Successive Parliaments have made people in New Zealand desperate, taken more and more money through tobacco tax out of the poorest households in this country.
"It has done almost nothing to reduce smoking rates. What it has done is driven the supply of tobacco underground."