A spokesperson for the Federal Trade Commission told AFP on Thursday that it would not appeal the February 1 decision.
The courtroom loss was seen as a setback for FTC head Lina Kahn, who has been an advocate of imposing tougher scrutiny on Big Tech companies on antitrust matters.
The FTC filed a complaint in federal court in July, arguing that Meta was trying to unfairly buy advantage in the virtual reality (VR) market with the purchase of Within, maker of fitness app "Supernatural."
A US judge denied the request on February 1 but gave the FTC time to decide whether it would appeal its rejection.
"Today marks an exciting new chapter for Within and Supernatural, as we officially join Meta," said Within CEO Chris Milk on Twitter.
"We're elated for the opportunity to bring joy, awe, wonder, and a happier, healthier life to more people around the world," he added.
The social media giant said when the suit was filed that the FTC's move defied reality, and expressed confidence that its buy of Within would be good for VR users as well as developers who make apps in that market.
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