Sinclair, of whom a sentencing judge said the description "monster" was inadequate, died in March 2019 at top security Glenochil Prison, Clackmannanshire.
He had been sentenced to life imprisonment with a minimum term of 37 years for the murder of Christine Eadie and Helen Scott, both 17, in Edinburgh..
The case is so named because the victims were last seen alive leaving The World's End pub in Edinburgh's Old Town more than 40 years ago.
The sentence, in 2014, the longest ever imposed by a Scottish court, meant he would have been 106 years old when he was eligible for parole.
Stirling Sheriff Court heard on Wednesday that although Sinclair, 73, had died of natural causes, and no criticism of his care at the hands of either the Scottish Prison Service or the NHS had been made, it was obligatory for a fatal accident inquiry to be held into the circumstances.
Karon Rollo, procurator fiscal depute at the Scottish Fatalities Investigation Unit, told the court: "This is a mandatory inquiry because Mr Sinclair died in custody at Glenochil Prison.
"I should perhaps also say that his next of kin are aware of the inquiry but don't propose to participate or attend."
Sheriff Wyllie Robertson set March 4th for the fatal accident inquiry itself.
He said: "I have seen the medical records, prison records, and the autopsy report.
"It's quite clear from all the papers I have read and what has been agreed that he died of natural causes and there's no issue arising in relation to the care of the prison service or any other parties that had dealings with him.
"Unfortunately we still have to fix a hearing."
Ms Rollo said she would be seeking only "formal findings."
Sinclair died on March 11th 2019 - coincidentally on the same day that the BBC's Crimewatch Roadshow programme profiled the Worlds End murders.
It is understood that he had suffered a series of strokes.
Angus Sinclair killings
He was convicted of four killings, including the World's End murders, but was suspected of killing four more women in Glasgow the same year.
Sinclair, who grew up in Glasgow, was 16 when he carried out his first killing in 1961.
He raped and strangled seven-year old neighbour Catherine Reehill before disposing of her body, but he was released in his early 20s after serving just six years.
In 1977, six women disappeared after nights out, and were found dumped on deserted farmland or waste ground.
Four of the victims - Frances Barker, Hilda McAuley, Agnes Cooney and Anna Kenny - were killed in Glasgow.
Teenagers Helen Scott and Christine Eadie went missing after last being seen at the World's End pub on Edinburgh's Royal Mile in October 1977.
They were found dead six miles apart in the East Lothian countryside the next day.
Despite the biggest manhunt in Scottish police history, the identity of their killer remained a mystery for decades.
In 1982, Sinclair was jailed for life after he admitted 11 charges of rape and indecent assault.
Almost 20 years later, when he was being prepared for parole, a cold case review revealed that his DNA had been found on Mary Gallacher - who was murdered in Glasgow in 1978.
He was given another life sentence after being found guilty of her murder.
Following that case, police began to examine the link between Sinclair and several other unsolved cases.
He first stood trial in 2007, accused of killing Christine Eadie and Helen Scott, but the case collapsed due to insufficient evidence.
Then, following a change to Scotland's double jeopardy law, he was prosecuted a second time and found guilty of the murders in 2014.
The sentencing judge described Sinclair as a dangerous predator capable of sinking to the depths of depravity, and said the words "evil" and "monster" were inadequate for him.
Sinclair married trainee nurse Sarah McCulloch in Edinburgh in 1970, and two years later they had a son Gary whom they brought up in Glasgow.
On Wednesday an insider said: "It is entirely to be expected that his next of kin would want to snub him in death."