The state's border has been closed since April to prevent the spread of COVID-19, but will transition to a "controlled border" next weekend.
The High Court ruled the border closure was valid and did not raise a constitutional question.
Palmer and his company Mineralogy were ordered to pay costs.
Premier Mark McGowan described it as a "significant victory".
"I will always fight to protect the health of Western Australians," he said.
Palmer has been contacted for comment.
The Queensland billionaire is separately pursuing WA government in the Federal Court after the state took the unprecedented step of passing legislation to amend a State Agreement over Mineralogy's Balmoral South iron ore deposit to protect itself from a A$30 billion damages claim.