Five days earlier it had blocked the move, begun after the Socialist government had ordered the collection returned to Catalonia on the recommendation of experts, sparking huge controversy nationwide.
Last week, 79 crateloads of the documents, photographs and other memorabilia left the western city of Salamanca, where they were archived after the war after being seized by the forces of General Francisco Franco in Catalonia.
At first, the court backed the mayor of Salamanca in ordering the transfer halted as "an exceptional protective measure".
But on Thursday a panel of judges decided unanimously the part of the "Salamanca Archives" demanded by the Catalan authorities should be returned.
Those who oppose the restitution of the artefacts to Catalonia, mostly conservatives, say the transfer will encourage other regional authorities to ask for their own wartime archives back and claim that dismembering the archives will make research more difficult for historians.
They add a transfer could open the floodgates to a stream of demands on museums to return precious objects to their country of origin.