The much-loved West Australian animal ambassador was a zoo icon and had 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 on Wednesday evening surrounded by her carers in her night quarters.
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 the conservation work of Perth Zoo and build an elephant guard post in the Bukit Tigapuluh ecosystem in Sumatra in her name.
The fund will help conservationists monitor and protect one of the last remaining wild herds of Sumatran elephants.
A special memorial walk will open at Perth Zoo on Sunday so people can pay their respects to Tricia.
"I would encourage everyone to honour Tricia and say farewell by visiting the memorial walk," Mr McGowan said.
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