The painting moves to the Louvre in Paris for an exhibition in March.
The original hangs in the Parisian gallery so this will allow visitors to compare the two works.
A black layer of paint on the Prado copy was removed as part of the restoration process - this revealed details in the landscape which experts say is evidence the replica was made at the same time Da Vinci painted the original.
The restoration process took two years.
Too risky
Experts discovered that the Prado version was painted on a walnut panel. This wood was used for other small-format panels by Leonardo and his studio, including The Lady with the Ermine and Saint John the Baptist.
The high quality of the materials used in the creation of the Madrid version suggests that it was an important commission.
The Prado's Mona Lisa has been in the museum since it was opened in 1819.
The newly-revealed painting will be on display there until 13 March.
There are dozens of surviving Mona Lisa replicas from the 16th and 17th Centuries - when copying famous artworks was a thriving business.
The original painting, dating from the early 16th Century, is obscured by several layers of old, cracked varnish.
However, cleaning and restoration is thought to be too risky because the painting is fragile.
A lithograph of the painting also exists, which is unusual for an anonymous copy. Although there were elements that clearly distinguished the copy from the Louvre's version, the most striking point was the fact that until the restoration of the Prado's version, no landscape background was visible.
Conservators at the Museo del Prado in Madrid recently discovered that this copy of the Mona Lisa was painted by a pupil working alongside Leonardo da Vinci. The Mona Lisa is one of the most enigmatic and iconic pieces of Western art.
There are two versions, both in the Louvre, the second of which is commonly referred to as 'Bacchus'. The original painting of this is lost, but was last recorded in the French Royal collection at Fontainebleau in 1625. Leonardo painted a different composition of the subject in 1508.
Besides the black background, one other difference from the original is the woman in the copy has eyebrows and the Mona Lisa in the real masterpiece does not. Prado conservators removed the painting's dingy, black background to find – to their astonishment – a Tuscan landscape similar to that in the true Mona Lisa.
Introduction: My name is The Hon. Margery Christiansen, I am a bright, adorable, precious, inexpensive, gorgeous, comfortable, happy person who loves writing and wants to share my knowledge and understanding with you.
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