The PSNI will recruit an extra 308 officers and staff by April 2020 after getting £16.5m in Brexit funding from the Treasury.
In May, Chief Constable George Hamilton confirmed that a business case was being drawn up.
The force was also asking for new vehicles and other equipment.
Mr Hamilton said the money would be invested in "policing with the community and keeping people safe".
Policing Board chair Anne Connolly said it was "welcome that the chief constable's bid for additional resources has been successful".
We welcome the announcement of additional Brexit funding for @PoliceServiceNI which we will invest in policing with the community and #KeepingPeopleSafe. It will also allow us to recruit a total of 308 additional officers and staff by April 2020.— George Hamilton (@ChiefConPSNI) December 19, 2018
"Resources available to the PSNI and their allocation to day-to-day delivery of the policing service is one of the key issues that the board will be discussing with the chief constable in the new year and in the development of policing plans for the time ahead," she added.
PSNI Deputy Chief Constable Stephen Martin said the majority of the funding "would go into frontline policing in and around the border communities".
"That is uniformed officers, many of them operating in neighbourhood teams and local policing teams working with local communities, reassuring local communities through the Brexit period," he added.
Mr Martin said the funding was "certainly not going to be spent in hardening the border, or increased infrastructure", but was "about officers on the beat with local communities".
He also said some of the funding would go towards enhancing the force's ability to tackle organised crime, and that a portion would be spent on vehicles, IT and intelligence.
Northern Ireland Secretary Karen Bradley said the funding will help the PSNI "manage pressures and contingencies arising from EU exit preparations, reflecting the specific and unique concerns in Northern Ireland".
The Police Federation of Northern Ireland (PFNI), the association that represents rank-and-file PSNI officers, welcomed the announcement but said "funding needs to be kept under constant review".
"This allocation is welcome and allays some of our concerns," PFNI chairman Mark Lindsay said.
"Preparing for Brexit is a task of monumental proportions with many unknowns."