Elaine Doyle, 16, was found dead in a lane less than 50 yards from her home in Greenock, Inverclyde, 28 years ago.
John Docherty, 49, was today found guilty of killing the teenager as she was returning home from a disco in the town.
During the 50-day trial, prosecutors said Docherty, of Dunoon, Argyll and Bute, forced her to the ground and killed her. She had been strangled.
He 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 June 1, 1986.
Her body was found the next day in a lane off Ardgowan Street.
The prosecution was the first to go 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.
But after evading justice for nearly 30 years, jurors today found him guilty of the crime.
In a statement released through Police Scotland after the conviction, the teenager's mother Maureen Doyle thanked officers and staff 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 and 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."