The Federal Trade Commission has also asked the U.S. District Court for the District of Columbia to delay the closing of the deal pending the outcome of the appeal.
The FTC is seeking to block the $565 million acquisition, arguing that it would stifle competition and lead to higher prices in the premium organic food market. The companies say the deal won't hurt consumers because they also compete with conventional supermarkets such as Safeway Inc. and Kroger Co., which are selling increasing amounts of organic products.
U.S. District Judge Paul Friedman rejected the FTC's arguments in a ruling late Thursday and denied the agency's request to block the transaction. The legal basis for the ruling remains under seal because it includes trade secrets.
Whole Foods said Thursday it agreed with the FTC's request not to close the transaction before Aug. 20. The companies may complete the acquisition after that date if no delay has been granted, Whole Foods said.
Shares of Whole Foods jumped $2.07, or 5 percent, to $43.24, while Wild Oats shares rose $2.69, or 17.7 percent, to $17.90 in morning trading Friday.