Tony Blair was given copies of the documents on a Moscow visit in 1997 after negotiations between Moscow and London.
President Boris Yeltsin told the Prime Minister then that he would ask officials to start the necessary paperwork to send the original documents back to Britain.
They include 10 diaries by prisoners of war. Three of these were by British and seven by Commonwealth servicemen.
One of the British diaries was that of Michael Duncan, one of the few men to escape from a German prisoner-of-war camp and reach freedom. His diaries, two 100-page orange notebooks written in a neat pencilled hand and illustrated with sketch maps, were kept in a Russian archive.
Duncan was a lieutenant with the Oxfordshire and Buckinghamshire Light Infantry who was wounded and taken prisoner at Dunkirk.
He was awarded the Military Cross after his escape. By the end of the war he had reached the rank of lieutenant-colonel.
He died of a heart attack in 1983, aged 72. A copy of the diary has been returned to his son Peter.
"My father never really talked about the war, mainly because of the hellish time he had as a prisoner," said Mr Duncan, who lives near Edinburgh.
"It was as if he tried to put most of it behind him after all the terrible things he saw and the suffering he underwent."Reuse content