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.
“This last is important. Even in corporate environments, it is very difficult to remove an underling for incompetence if that underling has seniority and a long history of good performance reviews. As in government bureaucracies, the easiest way to deal with such people is often to “kick them upstairs”: promote them to a higher post, where they become somebody else’s problem.”