It comes just a year after Elena also got over a bout of flu.
The centenarian wished for "good health", with medical staff clapping as she left the hospital in Madrid.
"I make a wish for good health, may it never be missing. And everything should get fixed, for good," Elena said.
Alvaro Alejandre de Ona, a doctor at the hospital, said: "She is a 104-year-old patient, who lives at home, she is a survivor.
"We have had her admitted here mainly because of her age, it was something that worried us.
"We are very happy. It is always a joy to see something like this end very well."
Elena was in the COVID-19 ward at Gregorio Maranon hospital for 14 days, and is the 4,149th recovered coronavirus patient discharged from the facility.
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