Leeds must pay RB Leipzig 21m euros (£18.4m) after their appeal against the transfer of Jean-Kevin Augustin was dismissed by the Court of Arbitration for Sport (Cas).
Leeds had appealed against Fifa's ruling in June that they must honour their "purchase obligation" for the striker, who joined on loan in 2020.
Cas upheld Fifa's decision "in its entirety" and ordered Leeds to pay the first instalment of £5.9m.
Leeds say they will appeal.
The West Yorkshire club signed Augustin on loan from RB Leipzig in January 2020 with an obligation to buy the Frenchman for 21m euros on a five-year-deal if they secured Premier League promotion for 21m euros, due in three instalments.
Augustin, who now plays for Swiss side Basel, struggled with fitness and injury during his time at Elland Road, featuring for 48 minutes across three substitute appearances.
Leeds won promotion to the Premier League at the end of the 2019-20 season but disputed whether the "purchase obligation" for Augustin had been triggered as the Covid-19 pandemic had interrupted the campaign.
A Cas statement said: "The Cas panel has dismissed the appeal filed and confirmed the obligation of LUFC to pay to RB Leipzig the first instalment of the transfer fee, i.e. euros 6,740,174.
"Further to its deliberations, the panel held that the purchase obligation had been triggered at the end of the 2019-2020 season, even though the season had concluded later than expected due to the disruption caused by the outbreak of the Covid-19 pandemic."
The Premier League club said in a statement: "Leeds United are surprised and disappointed by the Court of Arbitration for Sport's decision.
"[It] not only contradicts the language and meaning of the contract but also the practices adopted in European football under Fifa regulations, due to the unique impact of the extensions to the season necessitated by Covid postponements.
"The club will now review carefully all of its legal options with a view to an immediate appeal."