Leonardo da Vinci’s famous drawing of a spread-eagled male figure, known as the “Vitruvian Man,” will soon travel to Paris to star in a blockbuster Leonardo exhibition at the Louvre Museum. It will make the trip as part of an exchange agreement signed Tuesday by the culture ministers of France and Italy, after many months of sometimes bitter negotiations.

The drawing — a study of the proportions of a human body — is one in a series of works that Italian museums are sending to the Louvre for a show to mark the 500th anniversary of the Renaissance master’s death. The show is set to open Oct. 24 and run until February.

As part of the swap, the Louvre will send Raphael masterpieces, including “Portrait of Baldassare Castiglione” and “Self-Portrait with a Friend,” to Italy for a 2020 exhibition of his work at the Scuderie del Quirinale in Rome.

The principle of an exchange of works by Leonardo and Raphael was laid down in a Franco-Italian summit held in Lyon, France, in 2017. But a diplomatic dispute that broke out between the two countries over the nationalist agenda of Italy’s previous government loomed over negotiations. Relations between the two sides soured further late last year, when Lucia Borgonzoni, then Italy’s undersecretary for culture and a member of the right-wing League party, questioned the logic of lending multiple Leonardos in a major anniversary year. “Leonardo is Italian, and he only died in France,” she said. Ms. Borgonzoni later told The New York Times that France was showing “a lack of respect” and treating Italy like a cultural “supermarket.”