The herbivore enjoyed her birthday on Tuesday with a pink hibiscus flower cake at her retirement home in northern Australia.
Australia Zoo, where Harriet has spent the past 17 years, says the Giant Galapagos Land Tortoise was collected by British scientist Charles Darwin in 1835, although some historians have disputed this.
But DNA testing vouches for her venerable age and her birth in the Galapagos.
There is no doubt over the age of Harriet - who for more than a century was thought to be a male and named Harry - and she is recognised by Guinness World Records as the world's oldest living chelonian, or reptile with a shell of bony plates.
"She would definitely be the oldest living animal on Earth ... I can't see why she shouldn't live till 200," Australian conservationist and television celebrity Steve Irwin, who owns Australia Zoo north of the city of Brisbane, told Guinness World Records.
Harriet has not far to go before she beats the longevity record of 188 years set by another Galapagos-born tortoise that, until his death, was the pride and joy of the King of Tonga.
"We're well and truly hoping that Harriet lives a lot longer than that," keeper Laura Campbell said.
Irwin and his zoo staff have cared for Harriet since 1987, prior to which she had been at Fleay's Fauna Sanctuary for 35 years.