The vulnerable woman vanished in December 1999 but it did not become apparent she was missing until October 2016.
Edward Cairney, 77, and Avril Jones, 59, her supposed carers, were arrested a year later and in July 2019 were convicted of her murder.
Cairney and Jones were each sentenced to life imprisonment with a minimum term of 14 years.
The Inverclyde Health and Social Care Partnership confirmed on Thursday Professor Jean MacLellan has been appointed to head up a significant case review.
Prof MacLellan, a social worker by background, is the current director of Autism Network Scotland and has worked in a variety of local authority roles.
A spokesman said: "We have always been very clear that there will be a full independent inquiry into the circumstances surrounding Margaret Fleming's tragic death.
"However, the legal process had to run its course first.
"We were advised by the procurator fiscal that the inquiry couldn't start until the trial of Edward Cairney and Avril Jones, and any subsequent appeals, were complete.
"We have now appointed Professor Jean MacLellan OBE to head up the significant case review (SCR).
"The inquiry's first planning meeting is scheduled for February."
He added: "This will be a full, independent inquiry which will involve all the agencies which were involved with Margaret during her life.
"The final report will be published when it is complete. We expect that this will take some six months.
"A key area for the SCR team will be to uncover any lessons that are to be learned from the extensive cover up carried out by Edward Cairney and Avril Jones to hide their appalling treatment of Margaret, while she was in their care, and the murder that they subsequently committed."
The body of Ms Fleming, who had learning difficulties, has never been found despite numerous appeals to Cairney and Jones.
Jones was also convicted of fraudulently claiming £182,000 in benefits by pretending Ms Fleming - who would now have been 39 - was alive.
The couple were both convicted of perverting the course of justice.