Until now, New Zealanders could only be targeted by the agency if they were an agent of a foreign power.
A "Type 1" intelligence warrant will be needed to target New Zealanders using otherwise unlawful activities, such as intercepting phone calls.
That will require approval from the minister and a Commissioner of Intelligence Warrants and will be subject to review by the Inspector-General of Intelligence and Security - a process known as a "triple lock" process.
There will also be new flexibility in terms of getting warrants, including allowing warrants for classes of people rather than named individuals.
The Government has given the example of the intelligence agencies being alerted to a group of unidentified New Zealanders in Syria.
A group warrant would allow them to target those people without having exact information on their identities.
Urgent warrants can also be sought in special cases, including where someone's life is at stake or there is a serious threat to New Zealand's national security.
In such cases, a warrant must still be applied for within 24 hours, and if it is not authorised all information collected would be destroyed.
The reforms also create a new offence for leaking Government information, punishable by up to five years' jail.
The law changes were informed by a broad-sweeping intelligence review by Sir Michael Cullen and Dame Patsy Reddy, released last March.