Darlene Avis Geertsema, 30, was last seen at her family home in Devonport on the night of October 23, 1978.
Her red Holden was found abandoned near an oval in the northwest city a few days later.
An inquest held in December examined the original police investigation and Ms Geertsema's relationship with partner John Shepherd, who was described in hearings as a person of interest.
In findings handed down on Friday, coroner Simon Cooper ruled out suicide and misadventure as reasons for her death.
"On the evidence at the inquest the only person with the means and motive to have killed Ms Geertsema was Mr Shepherd," he wrote.
Mr Shepherd denied being involved in her death when he gave evidence at the inquest and no criminal charges have been laid.
Mr Cooper ruled Mr Shepherd had a history of frequent violence against several intimate partners, including Ms Geertsema.Â
Mr Cooper said Ms Geertsema had plans for the future that did not involve Mr Shepherd, who had exhibited jealousy and possessive behaviour towards her.
"For all these reasons I am satisfied to the requisite legal standard that Ms Geertsema died as a result of injuries inflicted upon her by Mr John Shepherd on the evening of 23 October, 1978," he wrote.
The coroner was unable to determine where Ms Geertsema died, the nature of injuries or what happened to her body.
Tasmania Police were unable to ascertain a motive for Ms Geertsema's disappearance at the time, and in 2013 opened a review into the case.
A $500,000 reward was offered in November for anyone with credible information that could help "uncover the truth".
27°C