The world governing body's decision is another blow to Roy Hodgson's struggling side whose inability to score goals - Saturday's 3-0 defeat against Manchester United means they have managed two in their last six Premier League games - is the principle reason why relegation is looming.
FIFA's decision was also expected to disappoint Cousin who had expressed a strong desire to join the Cottagers while training with Hodgson's squad during the January transfer window.
His agent, Willie Mackay, revealed: "The truth is we're glad the saga is all over. In fact, Daniel has already spoken to Rangers manager Walter Smith and told him he'd prefer to stay at Ibrox rather than go to Fulham. He thought at first that going to the Premiership would be a big opportunity for him, but he has realised he has a far greater chance of achieving success at a club like Rangers."