"The cheque has cleared and therefore puts in motion the process of the transfer," said a Barcelona club source.
Barcelona must now deliver his transfer certificate to the Spanish Football Federation (RFEF) who will then pass it to the French Football Federation (FFF) for the Brazilian to be registered.
The certificate has to arrive with the FFF before Sunday if Neymar is to take to the pitch at the Stade du Roudourou this weekend.
"Once we receive confirmation from Barcelona, the transfer (certificate) will be (sent) immediately," a spokesperson for the RFEF said, according to AFP.
Neymar's move to the French giants that smashed the world record transfer fee was announced on August 3.
However, he had to watch last weekend's 2-0 win over Amiens from the stands as the administrative formalities of the deal were not completed in time.
Despite the delay in registering one of the world's best players, FFF president Noel Le Graet remained confident Neymar would be able to make his bow at the Stade du Roudourou.
"There is no reason for this hold-up to continue," he said, according to French sports daily L'Equipe.
"I do not doubt that this will be quickly solved."