One of the oldest-known elephants in the world, Tricia died at Perth Zoo on Wednesday night after a final bout of illness.
The Asian elephant was a zoo icon and much-loved West Australian animal ambassador, having welcomed visitors to the park south of the city for 60 years.
"Her stature and her grace were compelling," Premier Mark McGowan said.
"Tricia brought such joy to so many people, which is why it was important that in her final moments she was treated with love, dignity and respect."
Tricia recently suffered a decline in her health, including sleep and mobility issues. She died surrounded by her carers in her night quarters.
A special memorial walk will open at Perth Zoo on Sunday so West Australians can pay their respects to Tricia, with plans for a permanent memorial also in the works.
Fifty per cent of Sunday's admission fees will go towards a conservation fund named in Tricia's honour.
The zoo will search interstate and overseas for an open-range park that can house its two younger elephants, Permai and Putra Mas.
"We're not going to rush it. We're going to care for them in the immediate aftermath of Tricia's passing," Environment Minister Reece Whitby told reporters on Thursday.
"The prime concern will be their safety and welfare, so we want to get it right."
While confident Perth Zoo has "a long future ahead of it", Mr Whitby acknowledged it was no longer appropriate for housing some larger animals.
"You need a lot of room and when you can't provide that space, particularly for herd animals that want to be in groups with other animals, it's not the appropriate place," he said.
Perth Zoo has asked the community not to send flowers and instead help create a legacy for this "extraordinary animal".
The Tricia Tribute to Conservation Fund has been established to support Perth Zoo's conservation work and build an elephant guard post in Sumatra's Bukit Tigapuluh ecosystem in her name.
The fund will help conservationists monitor and protect one of the last remaining wild herds of Sumatran elephants.
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