GPS devices, which can be worn around the neck, clipped to a belt or attached to a key ring, will track the location of the patient, allowing family and friends to monitor their whereabouts, according to the report.
Tags are already used by around 100 local authorities to track patients, but it is the first time a police force has signed up to the scheme.
"The GPS will be very cost-effective to the police," explained Chief Inspector Tanya Jones.
"It will reduce anxiety for the family and really reduce the police time spent on this issue."
Colleague Suzie Mitchell added: "We regularly have to search for missing people with dementia.
"It is heartbreaking to see the torment that their families are put through ? and to see the impact it has on the person with dementia when they are found."
Pensioner campaigners criticised the plans as inhumane.
"It smacks of criminality," said Neil Duncan-Jordan, the national officer of the National Pensioners? Convention. "These people have done nothing wrong.
"There has got to be a more humane way of coping with somebody?s mental state, and, if it has got to that extreme level, it does beg the question: are there not proper facilities to care for people when they have severe cases of dementia?"