Former Lord Advocate Dame Elish Angiolini, who led an inquiry into previous practices at Edinburgh's Mortonhall crematorium, described the situation as a "great tragedy".
The scandal emerged in December 2012 when it was revealed that the council-run crematorium had buried or scattered the ashes of stillborn and newborn babies for decades without their relatives' knowledge. Families said they were told there would be nothing to scatter.
The practice took place at the site between 1967 and 2011.
Dame Elish's report, which runs to more than 600 pages, was published by the local authority today after parents affected by the scandal were given individual copies of the document.
It contains more than 20 recommendations, which the council said will be taken forward by it and other relevant agencies.
Dame Elish was appointed by Edinburgh Council at the start of 2013 to head an inquiry into the practices at Mortonhall after they were uncovered by child bereavement charity Sands Lothians.
It emerged then that parents were led to believe there would be nothing to scatter and the ashes were dumped in a "mass grave" in a so-called "garden of remembrance" at the crematorium.
The investigation, described as "extensive and complex", began at the end of April last year and grew as it went on. The number of cases referred to the probe increased from 130 babies at the start to 253 babies by its conclusion.
The report on the findings said that the parents involved wanted to know what had happened at Mortonhall, even if any remains of their baby could not now be located.
But it stated: "The outcome of this investigation will cause more pain and distress for most of the parents of the 253 babies who are the subject of this investigation.
"It cannot be said with any certainty what remains of which babies are interred in the garden of remembrance.
"The precise extent to which remains of babies have been mixed in with an adult cremation that followed the baby's cremation is also unknown but appears likely to be extensive."
The report goes on: "The only baby remains in this investigation that can be said for certain to be in the garden of remembrance are those of the non-viable foetus that was the subject of a communal cremation in 2013.
"Some others will also be there but it will never be known which babies are there, which babies may be in the land adjacent to the garden of remembrance and which babies are mixed in with the ashes of the deceased adult who was cremated immediately following the baby.
"The great tragedy of these events over many years is that many parents will now be left with a lifetime of uncertainty about their baby's final resting place."
The report spoke of an apparent belief at Mortonhall that the bones of foetuses and even stillborn and neonatal babies could not survive the cremation process, despite available information to the contrary.
The inquiry found "overwhelming evidence" that foetal bones do survive cremation, at least from 17 weeks gestation.
There was also a "long-standing and wholesale failure" to comply with the local authority's duty to keep accurate records of the cremation of stillborn and neonatal babies at Mortonhall, the report stated.
It concluded that the situation at Mortonhall stemmed from a failure to reflect changes in social attitudes over the decades and that there was a lack of meaningful supervision or leadership from senior management on the issue.
It said: "The extent to which practices in the cremation of foetuses, stillborn and neonatal babies at the Mortonhall Crematoria have failed to reflect the changes over the years in social attitudes and the corresponding need for greater care, sensitivity and transparency is partly a product of an inward-looking and isolated managerial approach at the operational level.
"That situation was allowed to persist because of an absence of meaningful supervision or leadership from senior management on this matter.
"Staff employed there for many years largely adopted practices and beliefs formed and fixed over several decades.
"They worked for many years under the direction and supervision of the same superintendent who also preserved such opinions.
"She was a manager with a lively concern for efficiency and cleanliness but an apparent aversion to change."
The report said staff told the investigation that they had discussed the possibility of getting a baby cremator at the site but were told by the council that it was not financially viable, although there is no record of those discussions.
It is "likely" that some of the ashes of some babies will have been mixed in with the next adult to be cremated the following morning or interred in the land adjacent to the garden of remembrance, the report said.
Among the 22 recommendations in the report are suggestions that Edinburgh Council review the manner in which the crematorium is managed in the future, with a robust system of audit and inspection in place.
It is also recommended that the location of the interment of the cremated remains of a baby should always be noted in crematorium records.
The Scottish Government should commission research to pinpoint best practice in achieving remains in the cremation of foetuses, stillborn babies and neonatal babies, the report said.
"Unless a crematorium can demonstrate their competence in achieving remains and show consistent evidence of the sensitive treatment of next of kin in such cases, it is recommended they should not be permitted to continue the cremation of these babies," it stated.
The council should also make "strong representations" to the Government at Holyrood to have the term "ashes" defined in law to avoid confusion.
Ministers should further "make clear by legislative provision the obligations and rights relating to the burial and cremation of non-viable foetuses and stillborn babies", the inquiry found.
A separate independent commission, led by former High Court judge Lord Bonomy, was set up to review policies and practice across Scotland in relation to the handling of ashes following the cremation of babies and infants.
His report is expected to be released in the coming weeks.
Last week, parents hit by the Mortonhall scandal said they were "stunned" that they had not been informed when Dame Elish's report was passed to Edinburgh Council.
Dorothy Maitland, operations director of Sands Lothians, one of the affected parents, said she was disappointed that no-one from the local authority had let her know they had the document.
In compiling her report, Dame Elish interviewed bereaved families, current and former members of crematorium staff, funeral directors, support groups and health professionals, as well as experts in anthropology, law and forensic accountancy.
As part of her recommendations, she suggest consideration should be given to consulting parents about the creation of a memorial to the babies they lost.
Edinburgh City Council chief executive Sue Bruce said: "On behalf of the council, I would like to offer my sincere apologies to the bereaved families for the distress they have suffered as a result of the practices at Mortonhall Crematorium.
"I realise that the past year-and-a-half has been very difficult for the families involved and wish to thank them all for their co-operation with the investigation and their contribution to the report."
She said she would work with colleagues to take forward the important recommendations.
"It is also clear from the recommendations that there are far-reaching implications regarding cremation practices and the legislative framework not just for Edinburgh but across Scotland and the United Kingdom and I will be working with the Scottish Government and other relevant bodies to address these concerns," she added.
"We will now consult with families and relevant organisations regarding their views on a suitable memorial.
"It is vital that we learn from this and look to the future. We must ensure that the highest possible standards are adhered to at Mortonhall and that nothing like this can happen again."
Public Health Minister Michael Matheson urged the local authority to implement urgently the inquiry's recommendations.
He said: "I am clear that no parent should ever have to go through a similar experience to those affected by practices like this, at any crematorium in Scotland.
"We are absolutely committed to changing the law and a wide-ranging bill is already planned."
He went on: "The findings from Dame Elish's report will be used to inform the wider national review and any recommendations for government will be looked at by the Commission as part of their investigation. This work is entirely independent of government and the Commission must be able to complete its work before we can decide on any next steps."
Scottish Labour's Kezia Dugdale MSP, described the report as harrowing.
"Reading it, I struggled to understand how what happened at Mortonhall could have occurred for so long unquestioned," she said.
"It reveals systemic failures at all levels, from the council to the NHS and Scottish Government. Often fuelled by ignorance or a degree of complacency - all of which have led to unimaginable distress to those who lost their babies."
Scottish Liberal Democrat health spokesman Jim Hume MSP said: "The recommendations and findings of this harrowing report have far-reaching implications for the whole of Scotland.
"If we are to ensure that all lessons are learnt and with permanence, the Scottish Government must provide the Infant Cremation Commission with the fullest of support to allow it to implement its recommendations without hindrance."