It means Colin Ross, who was the first person in Scotland to be given an order for lifelong restriction, can ask the parole board to free him next year, although appeal court judges warned the 41-year-old he may never get out of prison.
Ross was on the sex offenders register and under supervision and subject to an order banning him approaching women when he attacked school teacher Marty Layman-Mendonca, 57, in July 2006.
Ms Layman-Mendonca, from Vermont, had been hiking on the Great Glen Way when she was attacked. She spent three months in hospital in a coma before being flown back to the United States where she died a month later.
Ross appeared at the Court of Criminal Appeal in Edinburgh because the Scottish Criminal Cases Review Commission took up his case.
Appeal judges Lady Paton, sitting with Lord Mackay of Drumadoon and Lord Drummond Young, were told that, since Lord Wheatley sentenced Ross, the rules had changed.
Ross has become another lifer to benefit from the ruling obtained by paedophile Morris Petch and schoolgirl rapist Robert Foye, who challenged the way judges calculate the length of time life prisoners must serve in jail before they can be considered for release.
In a written ruling issued yesterday, Lady Paton said: "In our opinion, Ross is a very dangerous man."
In court, Lady Paton warned Ross: "We emphasise that, whatever punishment part is substituted, it does not follow that you will be released into the community once that punishment part has expired."