Colin McIntyre, 44, is said to have made the statement to police more than 27 years ago after Elaine's body was found in Greenock.
Mr McIntyre told the court he had been blamed for strangling the naked girl when a sex session went wrong.
The statement, read to the High Court in Edinburgh, told how Elaine, 16, fell to the ground during a struggle as four youths gathered round her.
The account continued: "Wilks then picked up a piece of string and put it round her neck.
"She was face up. He put his knee over her and started pulling the string. He must have pulled it too tightly."
Bryan Wilkins, 45, who lived in Greenock in 1986, returned to Scotland from his home in Yorkshire to give evidence at the trial of John Docherty, 49.
Docherty denies murdering Elaine and has given the court a list of 41 possible suspects which, he says, might include the real killer.
Mr Wilkins said he knew his name was on that list - but he had never previously been confronted with the allegation he had strangled the girl.
Mr Wilkins said he was "on nodding terms" with Elaine and had been questioned by police after her death.
Asked if he told them the truth about his movements on the night she died, Mr Wilkins replied: "Absolutely, yes."
Defence QC Donald Findlay told Mr Wilkins he was named in the police inquiry not just as someone involved, or someone who was present. "You were named as the killer of Elaine Doyle."
Mr Wilkins told the lawyer: "I was not aware of that."
He told the trial that in 1986, when he was either a trainee plumber or joiner, his nickname was Vulch - short for Vulture. He added: "I have never been known as Wilks."
He said he could think of no reason why Mr McIntyre should tell police he was the killer and could think of no reason why police should want to blame him.
Mr McIntyre was someone he would meet at a local pool hall or an arcade in the town's Argyle Street, but not a close friend.
Mr Wilkins said he did not hang around with the other youths named as being present when Elaine died.
"A horrendous allegation," suggested Mr Findlay. "Absolutely," agreed Mr Wilkins.
Docherty, now of Dunoon, claims that at the time he is alleged to have stripped and strangled Elaine he was with his parents - who are no longer alive - at their home in Anne Street.
Docherty has also lodged a so-called special defence of incrimination claiming the culprit might be among a list of 41 names taken from files of the police investigation into the murder.
The trial continues next week.