Kerryn Tate's charred body was located in dense bushland near Canning Dam, southeast of Perth, on December 30, 1979.
The 22-year-old was last seen alive on December 29 when a friend dropped her home after a surf club party a night earlier in the Cottesloe and Swanbourne area.
DNA evidence has now linked Terence John Fisher, who died in 2000, to the crime scene.
Investigators believe Ms Tate planned to travel to a suburb near the bushland area to house-sit for friends but never got there.
Western Australia police previously said a fire swept through the area after Ms Tate's body was dumped about 800m from the Brookton Highway.
Detectives have named the former soldier as a suspect in the murder and believe he may be linked to the deaths of two other women.
Investigators said if Mr Fisher were still alive, he would have also been quizzed over the 1986 death of Barbara Anne Western and the 1991 death of Kerry Suzanne Turner.
Acting Assistant Commissioner Paul Coombes said the motivations for Ms Tate's "horrific" murder may never be known.
"In the 45 years since the tragic death of Kerryn Tate we have never stopped trying to find the person responsible," he said on Thursday.
"With the public's help we may be able to finally bring some comfort to the Tate family."
Detectives are attempting to build a picture of Mr Fisher's regular movements and routine, saying information from the public "could be the final key to solving one of WA's most notorious cold cases".
Police said Mr Fisher, who lived in Rivervale and the Manning areas in 1979, was a carpenter by trade.
He also regularly attended a sailing club in Fremantle.
Ms Tate had been living in WA for about a year, having left her home in NSW.
She worked in the arts and was known to often hitchhike. She was described at the time as a social woman with many friends.
Police have previously rejected a theory Ms Tate's death could have been linked to witchcraft, a rumour that was prominent in the years after her body was discovered.
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