Russian authorities have said a London exhibition of major Russian and French artworks should now go ahead.
The paintings will be kept in Moscow until the law is enforced
The country pulled out over worries the paintings, including works by Van Gogh and Matisse, would be impounded because of disputes about their ownership.
But Russia's Culture Agency has agreed to export the works once a new law is implemented guaranteeing their safety.
British Culture Secretary James Purnell announced on Thursday he would push the legislation through in early January.
From Russia: French and Russian Master Paintings is due to open at the Royal Academy of Art on 26 January.
Some of the 120 paintings included in the exhibition had been taken from private collections after Russia's 1917 revolution.
It was thought some of them could be seized to settle private legal claims.
Natalia Uvarova from the Russian Culture Agency said the paintings would be released for export, provided the British government's Tribunal Courts and Enforcement Bill 2007 ensured "the art's immunity from seizure".
Royal Academy said it wished "to express its gratitude to the Department for Culture, Media and Sport for their support for the exhibition and for making it possible".
Both governments have denied the clash related to the fall-out from the murder of former KGB agent Alexander Litvinenko in London last year, which has led to strained relations between the two countries.
The exhibition is currently in Dusseldorf, Germany, and had been due to come straight to London to be displayed in January.
The paintings will return to Moscow until the British law, which was passed earlier this year, is put through parliament when MPs return on 7 January.