John Docherty, 49, was told he must spend at least 21 years in jail for the murder that baffled detectives for almost 30 years.
He killed the 16-year-old as she walked home from a night out 28 years ago. Her naked body was found yards her Greenock home in 1986.
Elaine's devastated family - including her mother Maureen - made no comment as they left court this morning.
Elaine's brother John, who sat through more than 50 days of evidence, was also in court to see Docherty jailed for life.
Almost two months ago, a jury found Docherty guilty by a majority verdict of the murder of jewellery assistant Elaine.
Elaine had been for a night out at the Celtic Club in the town's Laird Street and was found dead the following morning in a lane.
Her murder featured on the BBC Crimewatch programme three years ago, and was one of Scotland's longest-running unsolved murders.
It was said to have "cast a long shadow" over Greenock.
In a statement after the verdict, Elaine's mum, said: "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-today 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."
Docherty is behind bars after police took 4500 witness statements and 722 DNA samples, and carried out 2500 door-to-door inquiries.
He was put there by two pieces of evidence which detectives initially did not realise they had.
The breakthrough came 25 years after Docherty pounced on Elaine, stripped her and strangled her.
Docherty, then 22, followed Elaine after the night out before launching a murderous attack.
She had phoned her parents to tell them when she would be home but when she hadn't appeared hours later, they feared the worst.
The next morning, June 2, her body was discovered naked in the lane.
Police believe the motive for the killing was sexual, but no evidence that a sex attack took place was discovered.
The prosecution of Docherty, from Dunoon, was the first to go to court following an investigation by the Crown Office's cold case unit, set up in 2011.
After the verdict, the Doyle family also thanked Frank Mulholland, the Lord Advocate, and all the police officers and staff who had worked on the case.
A second tragedy hit the Doyle family when Elaine's nephew was killed.
Jack Doyle, 17, was stabbed through the heart during a party in Greenock in January 2012.
His father, Elaine's brother John, has tattoos on either side of his neck, in memory of his son and sister.
Steven McIntyre was convicted of murdering Jack when a jury rejected his claim that he had been acting in self defence.
McIntyre, then 19, was ordered to serve at least 15 years of a life sentence before he could ask the parole board to free him.
Jack's shattered grandfather - and Elaine's dad - died three days after the 17-yearold was stabbed to death.