The new scheme means officers will be permanently based at Forth Valley Royal Hospital, Larbert, and at Polmont, Glenochil and Cornton Vale prisons from Monday.
Police Scotland said the initiative is aimed at helping hospital and prison staff deal with incidents and reducing fear of crime.
Superintendent Kenny Macleod said the scheme would “make our communities safer, make ourselves more accessible to more people and provide an efficient visible police presence at each of these busy locations”.
NHS Forth Valley medical director Tracey Gillies said: “This is an excellent example of joint working between the NHS, the prison service and local police.
“It will not only make it far quicker and easier for the police to gather statements but also provide a visible, accessible and reassuring police presence to our staff and the thousands of patients and visitors who attend the hospital every day.”
The move comes after police were drafted in to Dumfries Infirmary to help protect staff from attacks.
An officer has been stationed at the hospital since 2009 in response to incidents involving patient aggression.