The foxhound was deliberately run over near Conwy in February after police could not bring it under control.
The review said no action should be taken against the officers involved.
But it also recommended the force should introduce new procedures for dealing with similar incidents in future.
Traffic police drove at the dog at high speed on the dual carriageway between Llanfairfechan roundabout and the Conwy tunnel in the early hours of 22 February.
Firearms officers were sent to the scene, but there was concern they would not be able to get a safe shot.
The dog had gone missing from a hunt and police said the owner supported the force's decision.
The force voluntarily referred the incident to the Independent Police Complaints Commission because of the level of public concern.
The IPCC determined that North Wales Police should continue with its own investigation and advised on the makeup of the review panel, which included a vet, a representative of the RSPCA and a senior officer from the Metropolitan Police's Dog Support Unit.
The review has also recommended that patrol vehicles should carry slip leads and nets, which may have helped in this case.
Officers should get expert advice from dog handlers and vets if a similar situation happens again, it said.
Deputy Chief Constable Gareth Pritchard said: "It is regrettable that the dog died in this way and I fully understand the level of public concern.
"I am grateful to the panel who gave their time and expertise to carefully consider all aspects of the incident and for their diligence in coming to their conclusions and recommendations, which along with the learning points are being put in place by the force."
Officers were justified in using a patrol car to kill a dog running loose on the A55, a review for North Wales Police has said.