The International Automobile Federation (FIA)’s court of appeal also cleared Toyota and Williams, whose cars use similar ‘split-level’ rear diffusers and which rivals had claimed broke the spirit of the rules.
Button won the first two races of the season in Australia and Malaysia after overcoming protests from struggling champions Ferrari, Renault, Red Bull and BMW-Sauber.
The four teams had then appealed against the stewards’ decisions.
The FIA said in a statement that the court, which met in Paris for an all-day session on Tuesday, had decided "to deny the appeals submitted".
"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 statement added.
It said full reasons would be provided later.
Button and Brazilian team mate Rubens Barrichello will now be favourites to complete a hat-trick of Brawn victories at this weekend’s Chinese Grand Prix in Shanghai, the third round of the season.
Had the verdict gone against the three teams, Button could have been stripped of his wins with the championship thrown into turmoil.
Instead, rival teams will now be racing to catch up with radical redesigns of their own cars.