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The public will be able to see the items as part of a new display which will open at V&A East Storehouse, external from 2025.
The agreement between the museum and Yemen was signed on Tuesday by the director of the V&A, Tristram Hunt, and Yassin Saeed Noman Ahmed, ambassador for the Republic of Yemen based in the UK.
The V&A will take responsibility for the care of the stelae temporarily, until it has been decided that it is safe to return the objects to their country of origin.
The objects are of the type listed on the International Council of Museum's emergency red list of cultural objects at risk.
Mr Hunt said that he was "delighted" at the agreement.
"This is an historic agreement that will give the public the chance to appreciate these exceptional examples of Yemeni culture and creativity, before the objects are repatriated, and shine a light on how the V&A's Culture in Crisis programme helps curtail the illegal trade of looted objects and the preservation of cultural heritage worldwide," he said.
Charles Harper, UK charge d'affaires and deputy ambassador to Yemen, said: "Arts and culture can play an important role in rebuilding a society from conflict and this agreement is a fantastic way to ensure Yemeni culture remains in Yemeni care."
The V&A's Culture in Crisis, external programme was established in 2015 and looks to protect cultural heritage by working closely to support law-enforcement around the world to help prevent the illicit trade of cultural artefacts.
The stones will go on show at V&A East Storehouse, which is one of two new V&A East sites currently under construction in Queen Elizabeth Olympic Park.