Mr Scott was in court last November to see Angus Sinclair jailed for life after being found guilty of the 1977 murder of Helen and her friend Christine Eadie.
Giving evidence at the five-week trial, Mr Scott said he had promised his wife, who died in 1989, he would fight to the end of his days for justice for the girls - who were just 17 when they were killed after a night out at Edinburgh’s World’s End pub.
Mr Scott died on Friday aged 85.
Sinclair’s conviction secured justice for the victims’ families after almost four decades - and made legal history in the process as it marked the first prosecution since changes to Scotland’s centuries-old double jeopardy law.
The legal change meant Sinclair, who has been in jail since the 1980s, could be retried after the court case against him collapsed in 2007.
The teenagers were targeted by Sinclair and his brother-in-law Gordon Hamilton, now dead, on a night out on October 15 1977. Their bodies were discovered the following day, having been dumped in remote locations in East Lothian.
At the High Court in Livingston, judge Lord Matthews said the words “evil” and ‘’monster’’ were inadequate for Sinclair, as he ordered him to spend a minimum of 37 years in jail for the crimes - the longest sentence ever imposed by a Scottish court.
Speaking after sentencing, Mr Scott branded his daughter’s killer a “beast” and said the two girls could finally rest in peace.
DNA advances lead to the case getting to court again and it was prosecuted by Lord Advocate Frank Mulholland QC.
Mr Mulholland was among those to pay tribute to Mr Scott on Sunday.
He said: “I am saddened to hear of Morain’s death. Morain was a lovely man who bore his daughter’s murder with great dignity and forbearance.
“He never gave up hope that one day Helen’s murderer would be brought to justice. I was pleased to play a part in this and that this happened during Morain’s lifetime.
“I know that he promised his late wife that he would do everything in his power to achieve this. He made good on his promise. May he rest in peace.”
Mr Scott was honorary president of the East of Scotland Football Association, who said: “It is with great sadness that we have to announce our honorary president, Morain Scott, passed away on Friday evening.
“Morain was a very long standing servant of East of Scotland Football and will be sorely missed in our Association and League and, of course, at his club Coldstream FC.
“Our thoughts are with Morain’s family at this sad time.”
Civic Service Stollers FC said a minute’s silence would be held as a mark of respect before the side’s game next week.