In 2014, the Bonomy Commission reported on the treatment of baby ashes and recommended new laws and guidelines to protect bereaved families.
The Infant Cremation Commission, chaired by Lord Bonomy, made 64 recommendations, including an urgent review of cremation practices.
They include a statutory definition of ashes and regulation of cremation of babies of less than 24 weeks gestation.
The Scottish government has established a national investigation team to look into all the families allegations.
Public health minister Michael Matheson told the Scottish Parliament the team would be headed by former Lord Advocate Dame Elish Angiolini.
“The Infant Cremation Commission has made important recommendations to ensure that never again will any parent have to experience the pain of not knowing what happened to their baby’s ashes.
“However, I am acutely aware that, for many parents, questions remain about what happened in the past and that some still want their individual cases looked at.”
Patrick McGuire, from Thompsons Solicitors, who represents more than 200 families affected by the baby ashes scandal, said: “This announcement from the minister is very welcome.
“It’s what the families that I represent have been asking for. Dame Elish Angiolini did an excellent job investigating malpractice at Mortonhall crematorium and we have no doubt that she will do the same with her recently announced National Investigation Unit.
“The families are particularly pleased that she will look closely at each individual case and as far as possible give every family the answers they are looking for.
“We are also reassured that those people across Scotland who are identified as being responsible for this scandal will now be properly held to account. ”
Lord Bonomy’s report also said better records were needed in hospitals, funeral parlours and crematoria.
It recommended a national code of practice for infant and baby cremations and said an independent inspector should be appointed to monitor working practices at crematoria.