Justice secretary Keith Brown said the Scottish Government accepted “in principle” all of the recommendations contained in an expert report.
The Independent Review of the Response to Deaths in Prison Custody followed two years of research, analysis and engagement with families affected by deaths in custody, as well as prison and NHS staff.
It recommended a wide-ranging set of “systemic, practical and compassionate” changes to radically improve how deaths in prison custody are responded to in Scotland.
The report said: “Two pillars of trauma-informed practice are choice and control.
“Our review showed clearly that families bereaved through a death in prison custody have neither.”
It said an independent investigation should be instigated as soon as possible after the death and be completed within a matter of months.
The review said this should be carried out by a body wholly independent of Scottish ministers, the Scottish Prison Service or the private prison operator and the NHS.
Speaking in Holyrood, Mr Brown said: “We accept in principle the review’s recommendations and will very carefully consider the detail of these and take forward as a matter of priority improvements with key partners that will effect change to improve the ways that deaths of loved ones in prison custody are experienced by bereaved families.
“This includes the key recommendation of an independent body separately examining every death in custody.
“We are committed to making improvements to the response to, and experiences of, families impacted by a death in custody.”
Mr Brown said a full update would be provided next summer.