Rangers chief executive Martin Bain was bitterly disappointed at the collapse of the deal: "It's been a frustrating time for all parties.
"We are disappointed that it has taken FIFA so long to make a decision.
FIFA rules only permit a player to play for a two teams in a season, but a high-profile exception was made for Liverpool midfielder Javier Mascherano who had already played for both Corinthians and West Ham.
While Cousin admitted his disappointment at the news, he reaffirmed his commitment to staying at Rangers as the club fights for domestic and European success.
"Obviously when I heard I had the opportunity to move to the Premiership and the offer was right both for myself and Rangers, it was difficult to turn down," he said.
"However, I made it clear all along that I have enjoyed my time at Rangers and I am more than happy to stay, fight for my place and help the manager and the rest of the squad compete for silverware this season."
A deal for the 31-year-old could be concluded in the summer, but much will depend on Fulham - currently languishing in 19th - avoiding relegation.