Officers working for the organisation dubbed the British FBI will be able to use the powers of a police constable and recover criminal assets from gangsters.
Sinn Fein opposed the extension of its remit because of concerns about accountability, which led to a long delay.
Director general Keith Bristow said: "We have consistently said the NCA is committed to protecting the people of Northern Ireland against serious and organised criminals as we do in the rest of the UK.
"Now, with the legislative process complete in Northern Ireland, we will work with our PSNI and law enforcement colleagues and get on with doing our duty."
It will not be involved in counter-terrorism operations in Northern Ireland but its remit includes organised criminality committed by paramilitaries, like smuggling, drug-dealing and counterfeiting.
The agency was established in October 2013 to tackle serious and organised crime across the UK.
Previously, its responsibilities in Northern Ireland were restricted to areas like customs, tax and immigration.
But under legislation passed at Westminster the covert agency took on responsibilities for fighting cross-border crime, child exploitation, people trafficking, money laundering and internet abuse.
It also has civil recovery powers and could be used to "follow the money" in cases like a massive illegal dump recently discovered near Londonderry.
Changes mean the new agency will have to adhere to the same Code of Ethics as the PSNI and co-operate with the Northern Ireland Police Ombudsman Dr Michael Maguire.
The Policing Board - which was set up under the Good Friday peace agreement to oversee the PSNI - will also have full scrutiny powers while the chief constable will have primacy over NCA operations.
The Home Secretary would not have veto powers, it was revealed.
PSNI chief constable George Hamilton said the additional capacity and expertise will help his officers keep people safe.
"As the NCA becomes fully operational, we will be working closely with our new colleagues to ensure opportunities are maximised to tackle serious and organised crime and apprehend offenders.
"At the same time, I will ensure that the accountability arrangements being agreed with the Policing Board are factored into every aspect of operational activity to deliver both public confidence and community safety."
David Ford, justice minister at Stormont's devolved assembly, said it would have a significant impact in the fight against organised crime.
He added: "It is important, of course, that it has appropriate accountability within our local framework and it has that with significant roles for the Board and the Police Ombudsman.
"As a UK-wide organisation, the NCA has a level of resources and specialisation that cannot be achieved at regional level.
"There is no doubt that additional pressure has been put on the PSNI because they have not been able to use the NCA's considerable expertise. That will no longer be the case."
Ombudsman Dr Michael Maguire said confidence in local accountability arrangements was key to the extension of the NCA's role.
"My office will now investigate all complaints about the conduct of NCA officers operating in Northern Ireland, from allegations of misconduct through to alleged criminality."