Dame Elish, appointed by Edinburgh City Council at the start of 2013 to lead an inquiry into previous practices at the Scottish capital's Mortonhall crematorium, made 22 recommendations.
Dame Elish interviewed bereaved families, current and former members of crematorium staff, representatives from funeral directors, staff from other crematoria, support groups and health professionals and took opinion from experts in the field of human anthropology, law and forensic accountancy.
The report, with annexes, extends to over 600 pages in total.
The council said it has redacted parts of the report in the two weeks since it received the document from Dame Elish.
Sue Bruce, council chief executive, 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.
"I would also like to thank Dame Elish Angiolini and her team for their hard work on this important and sensitive investigation. Dame Elish has made many important recommendations, some of which relate directly to working practices at Mortonhall.
"I will be working with Council colleagues and elected members to take these forward."
She added: "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.
"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."
All families involved have been sent a copy of the report by courier this morning along with an individual case summary containing details of their case.
One section of the report relates to individual cases containing personal and sensitive information about the families involved.
Having taken legal advice and consulted with the Office of the Information Commissioner, the council said it has made redactions to this section to protect the privacy of these families and third parties.
The baby ashes scandal emerged in December 2012 when it was revealed that the council-run crematorium had buried or scattered the ashes of babies for decades without their relatives' knowledge.
Families said they were told there would be nothing to scatter.
The practice, which was discovered by child bereavement charity Sands Lothians, was carried out for 45 years and it is believed it ended at Mortonhall in 2011.
Since the revelations emerged, some other local authorities have also been implicated.
Affected parents and other campaigners have repeatedly called for a full public inquiry into what happened.