The head of the Roskultura agency, Mikhail Shvydkoi, told Russian news agency Interfax he saw no further obstacles to the From Russia exhibition going ahead at the Royal Academy of Arts in London.
"There's nothing to prevent us sending the exhibition to Britain. The exhibition will open on January 26," Shvydkoi said.
Russia had threatened to call off the exhibition, sponsored by German energy company E.ON, due to worries that people with claims on some of the 120 paintings could try to seize them.
The dispute reflected tensions between the two countries over several issues, including the 2006 murder in London of former Russian agent Alexander Litvinenko.
In a statement, the culture agency confirmed that permits had been granted for the four participating Russian galleries to send the art works to London.
"On the basis of state guarantees provided by Britain of judicial immunity for exhibits of the From Russia exhibition, permits have been provided by Roskultura," the statement said.
In response to Russian concerns Britain last month changed the law to prevent the seizure of the paintings by anyone claiming they were looted from their families in the 1917 Russian Revolution.
The works include paintings by Impressionists Paul Gauguin, Henri Matisse and Vincent Van Gogh as well as paintings by Russian artists.
They are drawn from Russia's four largest art galleries, including the Hermitage in Saint Petersburg and the Tretyakov Gallery in Moscow.
The dispute had prompted a diplomatic tussle between London and Moscow, whose relations have chilled after Russia's refusal to extradite Andrei Lugovoi, the chief suspect in the radiation poisoning of Litvinenko.
Britain and Russia are also embroiled in a row over Russian efforts to limit the work of the cultural arm of Britain's Foreign Office, the British Council.