Benrahma travelled to France on Thursday to complete a medical ahead of his expected move to the Ligue 1 side, but disaster struck late on deadline day when it appeared that the clubs had failed to complete the deal in time.
Benrahma had been due to join Lyon on loan until the end of the season, before signing on a permanent transfer in the summer worth more than £15million.
West Ham issued a statement confirming that the transfer had not been processed in time, while Lyon were scratching in accusing the English club of a “lack of respect” over the delay to the deal.
However, speaking at a press conference on Friday afternoon, Lyon director general Laurent Prud'homme said the club’s appeal to Fifa to have the transfer belatedly ratified had been successful.
He told reporters on Friday: "[Benrahma] has been dreaming of coming to play with Olympique Lyon and you can imagine how upset he was. His mother, his family, in a situation of this sort.
"What we did was began a procedure with FIFA to investigate what has happened. We sent all the proof of the fact that we had put in the data, signed all the documents in time. We have the screenshots of all the time we put in the data on the TMS, it was 22:26 exactly, we were way in time."
Prud'homme then received a message during the press conference. He added: "It seems that Fifa has just accepted the validation of the match so right now our efforts are paying off. The French Federation has asked the Premier League to have seven days to accept. It seems that our efforts are bearing fruit."