“At over 3m (9.8 ft) long, he was an impressive animal, but he was truly a gentle giant,” its post said.
But as he “wasn’t quite himself” over the past week, a visit to the vet had been arranged.
“After taking everything into consideration, we made the incredibly difficult decision to put him to sleep,” the zoo said.
Its founder Shaun Foggett said called Albert “the most incredible alligator, a big old lovable chap who was so chilled”.
“His gentle parenting with his hatchlings was amazing to see, but no real surprise given his nature,” he said.
“He will be greatly missed by everyone, especially the keepers, both past and present, who have cared for him over the years.”
Crocodiles of the World thanked the alligator “for everything you gave us” and for being “such a special part” of its family.