The deal, which will be made permanent in the summer for around £15million, looked dead in the water on Thursday night when both clubs released statements confirming that it had not been processed before the deadline.
Benrahma had already travelled to France to undergo a medical and remained in Lyon on Friday as the clubs worked with FIFA in a bid to push the deal through.
Lyon initially blamed West Ham for Thursday night’s delay, publicly accusing the Premier League side of “incomprehensible behaviour” and a “lack of respect”.
West Ham are understood to be hugely disappointed by those claims, which the club feels are proven to be unfounded by the fact that the deal has now been approved.
The two clubs previously had good working relations, with the Irons having made then Lyon playmaker Lucas Paqueta their club-record signing two summers ago.
Both Benrahma’s transfer and that of Hammers winger Pablo Fornals to Real Betis were the subject of FIFA investigations on Friday, with the global governing body satisfied that the relevant paperwork had been completed in time.
Benrahma departs after three-and-a-half years and more than 150 appearances in claret and blue.
The Algerian scored from the penalty spot in the Irons’s Europa Conference League triumph over Fiorentina last term but has not found the net since and has been reduced to a peripheral role this season, sent off on his last West Ham appearance in an FA Cup upset by Bristol City.