The original early 16th century painting by the Italian Renaissance master is on display in the Louvre in Paris.
The Los Angeles Times reported conservators discovered the "Mona Lisa of the Prado" while restoring a work initially categorized as a later replica of the famous portrait.
Art experts have said the copy, which has long been in the Prado's collection but was obscured under layers of black over-painting, was crafted at the same time as the original.
"It is as if we were in the same studio, standing next to the easel," the Times quoted Gabriele Finaldi, the Prado's deputy director of collections, as telling reporters at a news conference. "This is very, very close to how the 'Mona Lisa' looked in 1505."
After the copy is shown at the Prado, it will go on display at the Louvre in March as part of the French museum's "Leonardo's Final Masterpiece" exhibition, the Times said.