Druk, who had been in declining health since 2014, was put down shortly before midnight on Tuesday.
She had been unable to stand on Tuesday morning but carers decided to allow fellow elephants at the zoo to spend the day with her and say their last goodbyes, as would happen in the wild.
Druk did not have children of her own but was an amazing "aunt" to ten young animals, the zoo said in a statement.
She was described as having a strong character while zoo staff also said she was particularly adept at snapping branches from trees.
At 49, Druk the elephant was the longest living mammal at the zoo to date.
In April, firemen were called to the zoo after Druk was pushed over by her herdmates and found herself unable to get up again.
Using a crane, the recue team was able to lift the animal to her feet and lead her safely into the indoor enclosure, where she was checked over by a vet.
The zoo said at the time that euthanasia would be considered if Druck showed signs of suffering.