The Scottish Govern-ment accepted the recommendations of the Infant Cremation Commission report by Lord Bonomy and is to establish a National Investigation Unit, led by former Lord Advocate Dame Elish Angiolini.
The unit will be able to investigate specific cases where babies have been cremated and no ashes returned to the parents.
Several mums and dads were in the Scottish Parliament to hear Michael Matheson, Public Health Minister, respond to the report and set up an Inspector of Crematoria to ensure rules and regulations are now being followed.
Mr Matheson said: "The National Investig-ations Unit will be able to get detailed forensic examination of each individual case and a comprehensive picture of what has and has not happened in our crematoria.
"I am sure all of us are united in making sure this never happens again and the legacy must be having proper safeguards in place."
The recommenda-tions also include ensuring all crematoria follow the same practices, having accurate recording of all cremations which should be publicly available and setting up a national commission to implement the recommendations.
Parents who are still awaiting answers about what happened to the remains of their babies welcomed the report and action.
Lorraine Marshall from Bellshill, North Lanarkshire, whose son Michael Murray died at only four days old, said it was "good news".
She said: "I am relieved this is now off our shoulders.
"I've visited Daldowie Crematorium to know about Michael's final journey, but I got different answers depending on who I spoke to.
"I am pleased Dame Elish Angiolini will be taking it on and I'm sure she will leave no stone left unturned."
She said after Michael died in 2001 she was told by the funeral director there would be no ashes as the baby's bones were too soft.
But then in April last year she was told Michael did have ashes.
She added: "We have been working hard for a year over this."
The parents left the Scottish Parliament with forms to complete to have their case investigated.
Opposition politic-ians welcomed the report. Scottish Lab-our's health spokes-man Neil Findlay said: "I welcome the recomm endations and hope their implementation will prevent any future repeat of the pain and heartbreak that families in Scotland have had to endure."