Elaine, 16, was found dead in a lane less than 50 yards from her home in Greenock, Inverclyde, 28 years ago.
John Docherty, 49, was yesterday found guilty of killing the teenager as she returned home from a disco in the town.
In a statement released after the conviction, Elaine’s mother, Maureen Doyle, thanked everyone who had worked on the inquiry for the past 28 years.
She said: “Particular thanks must also go to Mr Frank Mulholland, the Lord Advocate, who was kind to my late husband, Jack, when he met him three years ago and who has followed the progress of the inquiry since 1986, and Mr John Scullion, for prosecuting the case at court.
“The people of Inverclyde who have lived this nightmare with us for the last 28 years have always supported our family.
“The result at court doesn’t make our day-to-day living any easier – the pain doesn’t go away – but my son John and I take comfort that we now have justice for Elaine, which is all we, especially her dad Jack, campaigned for.”
During the 50-day trial, prosecutors said Docherty, of Dunoon, Argyll and Bute, had forced the teenager to the ground and strangled her.
Docherty had denied the charges, claiming someone else was responsible, but jurors at the High Court in Edinburgh convicted him of the murder by a majority verdict.
Elaine was last seen alive by two friends after she left the disco in the town’s Laird Street on 1 June, 1986. Her body was found the next day in a lane off Ardgowan Street.
The prosecution went to court following an investigation by the Crown Office’s cold case unit, which was set up in 2011.
Strathclyde Police launched a fresh appeal over her death and Docherty was arrested in March last year.
He was charged with attacking her and removing her clothes before forcing her to the ground and placing a ligature around her neck and strangling her.
He denied the charges and lodged special defences of alibi and incrimination.
The case, which featured on the BBC Crimewatch programme three years ago, was one of the country’s longest-running unsolved murders and had “cast a long shadow” over the town.
Police spoke to thousands of people during the inquiry over three decades but it was advances in forensic science which helped catch her killer when evidence was examined 20 years later.
DNA found on Elaine’s back matched a profile for DNA found on her face.
Former soldier Docherty provided a DNA sample voluntarily in May 2012 and it was a one in a billion match.
Detective Superintendent Bobby Hendren said he was “extremely pleased” with Docherty’s conviction.
“This investigation has always been about Elaine Doyle and her family and bringing the man responsible for her murder to trial,” he said.
“I would like to pay tribute to her mum and brother, who have continued to support us throughout this investigation, and I am sorry that her dad is
no longer with us to hear the verdict.
“I can only hope that today’s verdict brings them some comfort.”
He added: “I, and all the officers who worked on this investigation, are well aware that the senseless murder of Elaine has cast a long shadow over the town of Greenock.”