The collector Shelby White has agreed to relinquish 10 antiquities that Italy claims were illegally excavated, the New York Times reported on Friday. Nine of the objects were turned over to the Italian Consulate on Park Avenue on Wednesday and will be shipped to Italy soon; Ms. White will hold on to one object, a 5th-century B.C.E. vessel signed by the painter Euphronios, until 2010, at which point she will cede it to Italy.

Ms. White and her late husband, Leon Levy, gave $20 million toward the construction of the new Greek and Roman galleries at the Metropolitan Museum of Art. Ms. White is a trustee of the museum and is on the search committee for a new director. The Leon Levy Foundation also donated $200 million to New York University to found an Institute for the Study of the Ancient World.

Two of the objects Ms. White turned over, the Euphronios vessel and a pot attributed to the painter Eucharides, were until recently on view at the Met.

The Times learned of the agreement, which was the result of 18 months of negotiations, from the Italian Ministry of Culture. In response to an e-mail from the Sun, Ms. White said through a spokesman that she was pleased with the resolution.

“From the beginning, Leon and I collected with the intention of preserving the past, so that people around the world could learn more about their history,” she said in a statement. “That’s why we have supported many facets of archaeology — excavations, publications, exhibitions, conservation, and education, and that is why we established the Institute for the Study of the Ancient World at New York University. Our collection was purchased at public auction and from dealers we believed to be reputable. In the case of the returned objects I believe I have taken the appropriate action.”

The Italians traced some of the objects in the Levy-White collection, including the Eucharides pot, to the dealer Giacomo Medici, who was convicted in 2004 in Rome of trafficking in illegal antiquities. In a 1995 raid on Medici’s Swiss warehouses, Italian investigators found numerous Polaroid photographs depicting classical objects, including some in the Levy-White collection, either broken or coated in dirt, as though just removed from the soil.

As part of the agreement, Italy agreed not to pursue other objects in the Levy-White collection that were catalogued for a 1990 exhibition at the Met, “Glories of the Past: Ancient Art from the Shelby White and Leon Levy Collection.”