Robert James Shaw Rodgers, 59 and from Tierney Gardens in Belfast, had denied the 1973 murder of teenager Eileen Doherty.
The 19-year-old woman was shot three times by a gunman after escaping from a hijacked taxi.
Last month, prosecuting QC Terence Mooney told the court Miss Doherty had been visiting her then fiancée Alex McManus, who lived just off the Ormeau Road area, when she went to the depot of Atlas Taxis at about 10.45pm on Sunday 30 September.
There were two other men in the depot also waiting for a taxi. The firm's owner, John Sherry said he would take all three at once but as he drove along Annadale Embankment, one of the men "pointed a gun at his head" and hijacked the taxi.
Mr Mooney said Mr Sherry shouted a warning to Miss Doherty and the pair ran but that the killers caught up with the teenager.
A witness who was cycling in the area saw a man get out of the passenger seat, grab her by the arm and heard "three or four shots" before he ran back to the car which then sped off.
The hijacked car was found the next morning and when it was examined, an RUC fingerprint officer found two palm prints matching Rodgers' right and left hands on the inside of the rear passenger window and on the steering wheel.
On Thursday, Belfast Crown Court judge Mr Justice Horner delivered his damning judgment that Rodgers was a secondary party in the murder and said it was "without a shadow of a doubt" he was finding the killer guilty.
He said there could be no possible innocent explanation for Rodgers palm prints being uncovered inside the hijacked taxi and that even if he had had any doubts at all, they were dispelled by evidence that less than a year later Rodgers had killed another young man, Ciaran McElroy, simply because he was a Catholic.
"Eileen Doherty was murdered because she was a Catholic who happened to be in the wrong place at the wrong time," declared the judge adding that despite the 40-year gap: "Murder is murder. The passage of time, whether it is five years or 55 years, in no way dilutes the seriousness of such a crime."
Jailing Rodgers for life, Mr Justice Horner continued: "I am satisfied beyond reasonable doubt the defendant assisted in the murder of Eileen Doherty.
"Although he did not pull the trigger of the gun that shot her dead, he was an integral part of the joint enterprise."
Mr Justice Horner adjourned fixing the minimum tariff until 15 March when probation and victim impact reports have been compiled.
Despite a bail application from defence lawyer Sean Devine who submitted that Rodgers had already served a significant life term and who would in all likelihood be subject to release after two years under the provisions of the Good Friday Agreement, the judge refused the application.
Mr Justice Horner told the lawyer that given the conviction for murder: "I have no power to grant bail...I'm not going to grant bail anyway as I do not think it is an appropriate case."
The PSNI Serious Crime Branch has welcomed the conviction.
Detective Chief Inspector John McVea from Serious Crime Branch, was the officer in charge of the renewed investigation.
"This case was reviewed by the Historical Enquiries Team before being progressed and taken to court by detectives from Serious Crime Branch after investigative opportunities were identified," he said.
"Everyone who worked on the case is pleased that a small degree of closure has been provided to Eileen's sisters and brother by today's conviction. It shows that, where there are investigative opportunities, police will work to bring offenders before the courts no matter how long ago a crime was committed."
He added that officers would "fully investigate" if further evidence came to light about the actual gunman who murdered Eileen.
Speaking outside the court Mrs Linda Marsden, one of Eileen's six sisters, said she hoped the guilty verdict would bring "some comfort" for the family.
"We have grieved for almost 40 years for our sister Eileen. Our Dad never came to terms with the murder of his daughter. He could not even speak her name. He was traumatised until his death in May 2012.
"Our mother, although traumatised, had to be strong and continued to care for her other seven children until her death in August 2009. As a family we have been given answers to questions that have tormented us. Who could have done this to a beautiful 19-year-old girl? She posed no threat to anyone."
Thanking the police and HET for their efforts, Mrs Marsden said she hoped Rodgers' conviction would bring "some sort of closure" to the family who were relieved that "justice has finally been done."