Sinclair spent more than half his life behind bars, originally being jailed in 1982 for sexually assaulting girls between the ages of six and 14.
He was also convicted of murdering 17-year-old Mary Gallacher in 1978, who was raped and stabbed near a railway line as she went to meet a friend. and eight-year-old Catherine Reehill in 1961, both in Glasgow.
The killer was ordered to serve a minimum of 37 years in prison for the murders of Eadie and Scott – the longest minimum sentence ever imposed by a Scottish court.
Detectives suspect he could have also been behind several unsolved murders from the 1970s.