Baby and adult ashes were mixed together at the crematorium and given back to relatives of the adult.
The parents of infants were told there were no ashes.
Aberdeen City Council's insurers are already dealing with claims, and a deadline for any more has been set for 1 February.
BBC Scotland revealed in 2013 that no ashes had been offered to the families of infants cremated in Aberdeen over a five-year period.
It followed similar revelations about Mortonhall crematorium in Edinburgh, which had been secretly burying baby ashes for decades.
A report into the scandal by Dame Elish Angiolini described the practices as "abhorrent".
Patrick McGuire, a partner with Thompsons Solicitors - the firm representing many of the families involved - said: "The past few years have been immensely painful and stressful for the Aberdeen families.
"They have struggled to get their concerns heard. They felt as if their concerns were being ignored and brushed aside.
"The fact that we are where we are today is a testament to their courage, tenacity and dignity as well as the knowledge that in the end they knew they would be proved right.
"Over the past few years myself and the Aberdeen parents have had no alternative other than to follow a course of being highly critical of the stance adopted by Aberdeen City Council. The council has now done the right thing and for that they should be given credit.
"Myself and the families also believe that the report produced by Dame Elish Angiolini into these terrible events was critical in bringing us to this point and we wish to extend our thanks to her."
A spokesperson for Aberdeen City Council said: "We are committed to moving towards a settlement of claims for compensation and are working with all parties to ensure the individuals and families involved in the process are kept fully informed throughout the process.
"The council has wholeheartedly apologised for the distress past practices at Aberdeen Crematorium have caused. The commitment to the compensation process is part of a full and comprehensive response from the organisation but Aberdeen City Council is clear that the impact on those affected must never be forgotten."
The terms of compensation packages will remain confidential.
Families affected by the baby ashes scandal at Aberdeen's Hazlehead Crematorium have been given a deadline for lodging compensation claims.