A man described as a “sexual predator” has been found guilty of a 1979 murder and five attacks on other women.
Sally McGrath, 22, was found naked in a shallow grave in woodland near Peterborough, Cambridgeshire, in March 1980 after vanishing in July 1979.
Her killer could not be found despite a major police investigation.
Former soldier and builder Paul Taylor, 60, originally from Peterborough and now of Valentine Close, Fareham, Hampshire, was arrested last year following a cold case review.
Today, at Chelmsford Crown Court, a jury found him guilty of murder following 23 hours of deliberation.
He was found guilty of three counts of rape, one attempted rape and a serious sexual assault, which were all committed in the months leading up to Miss McGrath's murder.
Mr Justice Owen told Taylor: "You have finally been brought to justice and you will now serve life in prison."
He commended Cambridgeshire Police detectives for solving the mystery, which officers at the time had failed to bring to court despite the force's biggest pre-Soham investigation.
Taylor will be sentenced tomorrow morning.
Cambridgeshire Police said it would now investigate possible further sex attacks committed by Taylor during the years he escaped justice.
Detective Superintendent Jeff Hill, who led the new investigation, said: "As a result of this inquiry, we have already considered what other offences may have been committed by Taylor.
"Given the nature of the offending, there is every chance that similar crimes have occurred that we just quite simply don't know about."
Taylor denied the charges, saying that all of the sexual incidents either did not happen or were consensual.
He claimed there were many other people who could have killed Miss McGrath.
Opening the trial, prosecutor Karim Khalil told the court Taylor was married at the time of the 1979 offences.
He openly slept with other women, regularly going for "quickies", but insisted in a police interview that the relationships were always consensual.
Describing Taylor as a "sexual predator", Mr Khalil added: "In the 1970s he was a reasonably good-looking and physically strong young man. He was brimming with confidence and had the capacity to be an engaging flirt and a ladies' man.
"But if he did not have his own way, he had the capacity to become violent very quickly.
"He used this violence to force young women into submission or simply have his way with them."
A statement was read outside court on behalf of Miss McGrath's parents, Christine and Joe, and the rest of the family.
It said: "We would like to express our thanks to Detective Superintendent Jeff Hill and all of the current members of his cold case team for their hard work, dedication and professionalism."
Speaking after the verdict, Mr Hill described Taylor as a "predatory sex offender" who brutally murdered a young woman with "her entire life ahead of her".
He said: "I would like to pay tribute to Sally's family who have retained their optimism and dignity throughout this entire process.
"I hope that the pain of the last 30 years will now, to some extent, start to subside.
"I would like to say that Taylor deserves every second of his imprisonment for the misery he has brought to so many lives.
"I pray that Sally can now rest in peace and hope that the message to anyone who is aware of this investigation is clear - the British police do not forget."