The deal includes an option for Lyon to make the deal permanent in the summer.
West Ham's announcement brings to an end a bizarre 18 hours after the deal was not completed by the transfer deadline.
Lyon accused West Ham of 'incomprehensible' behaviour and vowed to take their case to world governing body Fifa.
The Hammers have refused to respond to the allegations, but officials at the club are known to be furious at what are viewed as inaccurate and potentially damaging claims.
Given Fifa has now confirmed the deal, it is felt Lyon's statement was without foundation.