In return, the Louvre will send five works by Raphael to Rome next year for an exhibition at Rome's Scuderie del Quirinale museum marking 500 years since the painter's death.
French Culture Minister Franck Riester and his Italian counterpart Dario Franceschini signed off on the loans in Paris on Tuesday.
The exchange of Leonardo and Raphael artworks for the anniversaries had long been discussed between Rome and Paris, but Italy's previous right-leaning government played hardball on the issue.
The far-right League, in particular, was opposed to loaning the "Vitruvian Man" and other Leonardo works on the grounds that it was wrong to let the French dominate celebrations for an Italian artist.
"Leonardo was Italian, he only died in France," Lucia Bergonzoni, a former League junior culture minister, told the Corriere della Sera daily 10 months ago. "The French cannot have everything," she added.
Bergonzoni lost her ministerial position this month, as a change of government sidelined the League and its leader Matteo Salvini into opposition.
Salvini had sparred with France's liberal President Emmanuel Macron on a range of other topics, including migration and the future of the European Union.
In addition to the "Vitruvian Man," the Louvre will be loaned four other Leonardo drawings from the Uffizi Gallery in Florence, as well as two copies of Leonardo paintings.
But the artist's self-portrait in red chalk is not on the list, although Riester prematurely announced several months ago that it would be lent to the Louvre along with the "Vitruvian Man."
The Louvre will lend the Scuderie del Quirinale five Raphael drawings and two drawings by the artist's disciple Giovan Francesco Penni.
The loan to Italy also includes two Raphael paintings: "Self-portrait with a friend" and a portrait of Renaissance diplomat and man of letters Baldassare Castiglione.
Leonardo da Vinci, who was not only an artist but also an engineer, inventor, musician and philosopher, lived most of his life in his native Italy but spent his last three years in France at the invitation of King Francis I, a noted patron of the arts.
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