Paul Shakespeare, 66, grabbed the 18-year-old girl on the afternoon of Sunday 29 April as she was walking her dog along the Honeybourne line – a section of railway converted into a footpath.
Shakespeare of Scaleby Close in Upperby, Carlisle had armed himself with a sharpened stick with a nail driven through it, and forced the victim into nearby undergrowth where he raped her.
He threatened the victim – who was unknown to him – and told her not to tell anyone before fleeing the scene.
A full DNA match was recovered at the time but Shakespeare was never traced.
Despite renewed appeals for information in 2007 and 2008 by Gloucestershire Constabulary, Shakespeare was only tracked down when he was arrested for possession of a knife earlier this year.
After his DNA matched him to the rape in 1990, he was re-arrested on August 15 and subsequently charged with rape and possession of an offensive weapon in a public place.
He pleaded guilty to both charges at Gloucester Crown Court via video link on Thursday.
The investigating officer, Detective Constable Simone Bow,ley said: “Firstly I would like to commend the victim as her bravery and courage has been phenomenal right from the day this horrific crime took place, through to present day.
“She has had to wait for more than 30 years for Shakespeare to admit his abhorrent crimes.
“The case has been reopened and reviewed over this time, and she has continued to work with us in the hope that one day he will be caught and brought to justice.”
DC Bowley continued: “The impact of this crime was felt within the wider community, too, as people were fearful (after) what took place that day.
“We all had hope that we would be able to identify the man responsible for this, and I am glad that day has finally come.
“I have updated the victim on today’s outcome and she was relieved to hear the news.
“In Gloucestershire we have a dedicated rape and serious sexual offences team and I would urge anyone who has been the victim of a sexual assault, whether recent or non-recent, to please contact police or other support agencies and report it.”
Shakespeare was remanded in custody and will be sentenced on January 17 at Bristol Crown Court.