The changes come as part of what the police force has called the "biggest shake-up" in policing in years.
The PSNI said the teams will "deal with community problems" and give "advice".
The first LPTs to launch will be based in Lurgan and Armagh city police stations in County Armagh. They will be supported by four mobile neighbourhood policing teams (NPTs).
The roll-out of all 26 LPTs is expected to be completed by 1 October.
Assistant Chief Constable Stephen Martin said policing in Northern Ireland is in a process of "transformation" due to "significant budget pressures" and new council structures.
He said "normal policing will carry on" and the new teams will respond to calls, conduct investigations, and "deal with community problems".
"They will provide advice and reassurance and spend time learning about what most affects communities in order to work with them to improve safety and quality of life," he said.
The 34 NPTs, which will be based in areas with higher levels of crime and deprivation, are to be set up with the aim of providing "an additional dedicated policing presence, reassurance and commitment to communities where it is most needed".
ACC Martin said restructuring means the number of police stations currently in existence is under review.
"The reality is that nearly all policing services are delivered outside of stations," he added.
"Policing isn't about buildings it is about officers working with the community in the community."
The Police Service of Northern Ireland has started to phase in local policing teams (LPTs).