Pepe, who lived in a corral at the Galapagos National Park's Interpretation Center, died of natural causes, said the park's ecosystems director, Victor Carrion.
"Several of his organs had been slowly failing," Carrion told AFP, saying the tortoise was also overweight.
Park director Arturo Izurieta paid tribute to the tortoise on Twitter.
"After 60 years of life, Pepe the Missionary will remain in our memories forever," Izurieta said yesterday.
He brightened the post with a bit of good news for conservationists: "The disappearance of Pepe the tortoise does not put his species in danger."
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About 2,000 tortoises from the same species still live in their native habitat.
Pepe was adopted from the wild by a family from San Cristobal island in the 1940s.
Local fishermen named him "Pepe," which was then expanded to "Pepe the Missionary" when he was given to Franciscan missionaries on the island in 1967.
He became the missionaries' mascot and a beloved community pet, often photographed and fed by visitors to the mission.
The missionaries handed him over to the national park in 2012 -- the same year the reserve lost another famous tortoise, Lonesome George, the last known member of the subspecies Geochelone nigra abingdoni.