The Federal Trade Commission (FTC) voted four to one to drop an administrative complaint over the coal merger, citing a 2004 court ruling that denied the agency's request to block the deal.
Continuing the administrative complaint could amount to "an unproductive repetition of the same litigation" that led to the agency's defeat in court last year, commissioners said.
"We are ultimately convinced that the public interest would not be benefited by an administrative trial in this instance," the commissioners said.
After Arch Coal bought Triton's two mines, Buckskin and North Rochelle, as well as other interests from Triton, the FTC argued that the bigger entity would undermine competition among coal producers in Wyoming's Southern Powder River Basin.
US district judge John Bates ruled in August the FTC had failed to make the case for a preliminary injunction against the deal. The acquisition of Triton was finalised and the Buckskin mine later sold by Arch.
The FTC said it would continue to closely monitor competition among coal and other energy producers and aggressively enforce the antitrust laws against producers that engage in anti-competitive conduct.
