Sinclair, who was convicted of the notorious World’s End murders in Scotland, died overnight at HMP Glenochil in Alloa, Clackmannanshire.
In 2014, the convicted killer and paedophile was found guilty of raping and murdering teenage girls Christine Eadie and Helen Scott 37 years beforehand.
The pair, both 17, were brutally killed after a night out at Edinburgh’s World’s End pub on October 15 1977, with their bodies discovered the following day in East Lothian. They had been bound and strangled with their own underwear.
Sinclair was acquitted of killing the girls following a failed prosecution in 2007, but the case was the first to be retried under Scotland’s double jeopardy law seven years later.
Speaking today, Helen Scott’s brother, Kevin Scott, told Sky News: “I understand Sinclair’s health has been in decline for some time.
“For the barbaric way that he stole the lives of Helen and Christine there is a part of me that would have wanted to see him live to be punished and serve the 37 years handed down, he wasn’t strong enough for that, some may say it was the easy option.
“With the announcement of his death I feel for all the victims and families that Sinclair may have impacted on throughout his violent life, but will now never know.”
Sinclair, who was 73 when he died, spent more than half of his life behind bars for killing four girls as well as for a string of sex attacks on young children.
The first was in 1961 when, aged 16, he killed seven-year-old Catherine Reehill.
Following his release, he was sentenced to life in 1982 for a number of rapes and indecent assaults against young girls.
While still in jail for the sex attacks, he was convicted of the 1978 murder of Glasgow teenager Mary Gallacher.
The 17-year-old was raped and stabbed near a railway line as she went to meet a friend. Sinclair was linked to the crime years later following a DNA breakthrough.
Scientific advances later led detectives to Sinclair for the unsolved World’s End murders.
But detectives suspect Sinclair could have been behind several other unsolved murders from the 1970s.