Edward Cairney and Avril Jones, aged 77 and 59 respectively, killed Margaret, 19, in December of 1999 or January of 2000, a jury determined at the High Court in Glasgow after two days of deliberation.
Jones was also found guilty of fraudulently claiming over £180,000 of benefits over a period of nearly two decades by pretending that Margaret, who had learning difficulties, was still alive.
Authorities first became suspicious in late 2016 amid concerns over benefit claims that were made by Jones on behalf of Margaret.
An extensive and lengthy search, centring in and around the couple's home in Inverkip, near Greenock in Inverclyde, failed to discover Margaret, who her carers continued to maintain throughout their trial was still alive.
Cairney told the court that Margaret was living in London and returned to Inverkip intermittently when she needed money.
The jury convicted the pair, who became Margaret's carers after the death of her father in 1995, after a seven-week trial.