More than 450 people are feared to have had their lives shortened at Gosport War Memorial Hospital between the late 1980s and 2001, an independent report found last year.
Kent Police announced on Tuesday that the care provided to patients who died at Gosport would be the focus of its investigation.
Families were told of the decision at a meeting in Fareham shortly before the announcement was made.
Alongside the 450 who died, another 200 were “probably” similarly given opioids between 1989 and 2000 without medical justification, according to the Gosport Independent Panel report released last year.
Three previous investigations into 92 of the deaths by Hampshire Constabulary resulted in no charges being brought.
In July, the head of serious crime at Kent and Essex Police announced a review of the evidence which had emerged from the report.
A team lead by Assistant Chief Constable Nick Downing has been assessing the panel’s findings to establish if there is sufficient new evidence to support a further police investigation.
On Tuesday, Downing said: “The families of those affected by the events at Gosport War Memorial Hospital are at the heart of everything we do and I hope the news that we will now be carrying out a full investigation is of some comfort to them.
“This investigation is not about numbers, it is about people - specifically those who died at the hospital and the loved ones they have left behind.
“There have been three previous police investigations into deaths at the hospital. It was therefore important for us to carry out an initial assessment of the materials obtained by the Gosport Independent Panel to establish if it contained sufficient new information that has not already been submitted to the Crown Prosecution Service.
“Now that we have launched a full investigation, we will be arranging to meet with the families on a one-to-one basis and invite them to give statements on their own experiences with the hospital, as it is their accounts about the loss of their loved ones that will help put the medical assessments we have into context.
“This is a highly complex and emotive case that some family members have been living with for more than 30 years and I would like to thank them for their continuing patience and understanding during this process.”
When the independent report was published last year, Bridget Reeves - whose grandmother Elsie Divine, 88, died at Gosport in 1999 - said vulnerable relatives had been “stripped of their final words to their loved ones”.