A jury found Docherty guilty by a majority verdict of the murder of Elaine Doyle, whose body was found just yards her Greenock home in 1986.
The 16-year-old 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.
The prosecution of Docherty, 49, from Dunoon, was the first to go to court following an investigation by the Crown Office's cold case unit, set up in 2011.
Elaine's 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.
Docherty will face life in prison when he returns to the High Court in Edinburgh in August for sentence.
He 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.
Officers took a blanket from their police car and threw it over her body.
It was a blunder that was used in Docherty's trial to lead to claims that the crime scene was potentially contaminated.
Sticky tape-like strips were taken in a bid to extract evidence from the 16-year-old's body.
Forensic officers were looking for hairs or materials that might give them a lead on the killer. But, no clues were found.
The strips of evidence were sealed, stored away, and all but forgotten.
In 2005, a full review of the case was ordered. The clothes found next to Elaine's body were in torn bags meaning samples would be unreliable.
But the tape was sealed -and in a perfect condition.
Forensic analysts discovered DNA had been picked up from Elaine's body.
A full profile was obtained from strips taken from the victim's back, with the same man's DNA, mixed with Elaine's own, found on samples taken from her face.
Police trawled the database.
They were confident that someone who murdered a teenage girl, would have committed other offences in 20 years.
But the result came back negative.
After more than 700 people had been voluntarily tested, officers reached the name John Docherty.
He had been mentioned in a friend's witness statement, but was never spoken to by police.
Still living in Greenock with his long-time partner and young daughter, he appeared an unlikely suspect. Other than a housebreaking conviction as a teenager, his record was clean.
Detectives arrived at his door on May 12 2012. They asked him to give a DNA sample.
Docherty, a former Army man and council driver, complied without resistance.
Two weeks later officers were told that they had a DNA hit and that the chances of the result being wrong were one in a billion.
Finally, they had found Elaine's killer.
Justice had caught up with John Docherty.