The Premier League club had announced on the final day of the summer transfer window that a deal had been agreed in principle for the midfielder to join on a season-long loan, with the option to buy.
However, Fifa refused to ratify the move for reasons, as yet, unknown - but it is thought that the required paperwork failed to beat the transfer deadline in England.
A statement on Everton's official website read: "Fifa have today refused to ratify the loan transfer of Vadis Odjidja-Ofoe to Everton from Club Brugge.
"The decision comes despite both the Football Association and Premier League giving their full support to the loan agreement and Everton lodging the relevant signed paperwork in advance of the international transfer deadline on August 31."
Odjidja has admitted his disappointment at the collapse of the move and, with it, the opportunity to play in the Premier League, but has insisted it will not affect his work rate for his current side.
“I knew this could happen because Everton were late with their bid. Club Brugge did not want to let go of me, which I can understand," Odjidja-Ofoe told the club's official website.
“It would be a lie if I said that I did not want to play in the Premier League, but now I can look forward and know that there are still opportunities for me to take the next step.
“There are many options for me at Club Brugge, and I will still contribute and show that I am valuable to the club."