"Based on the arguments heard and evidence before it, the Court has concluded that the Stewards were correct to find that the cars in question comply with the applicable regulations," the FIA said in a statement following a Tuesday hearing in Paris.
This means that the Brawn, Toyota, and Williams teams can continue using their diffuser during the races. F1 race analysts have earlier said Brawn's two consecutive victories in the first two races of the 2009 series may be attributed to the "double decker" designs at the rear of the racecar.
The dispute over diffusers rose when BMW Sauber, Ferrari, Red Bull and Renault cast doubts over the legality of their use.
The FIA said the full reasons for its decision to junk the appeals of the four teams "in due course."
Both Brawn and Toyota said they were pleased with the decision of the FIA appellate court.
"The FIA Technical Department, the stewards at the Australian and Malaysian Grands Prix and now five judges at the International Court of Appeal have confirmed our belief that our cars have always strictly complied with the 2009 Technical Regulations," Brawn team principal Ross Brwan said in a statement.
Toyota likewise said it has complied with the technical rules of F1 and had been confident that its car is not violating any of the regulations.
"This has been a challenging period for Formula 1 and I am pleased this issue is now in the past and we can focus on an exciting season on the track," said Toyota team chairman and principal Tadashi Yamashina.
The next leg of the 2009 F1 series will be held in China from April 17 to 19.
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