The appeals court could have blocked the league's punishment of the pair, but it ruled that a diuretic in the weight-loss supplement StarCaps wasn't protected by workplace drug-testing laws.
Peter Ginsberg, Kevin Williams' lawyer, confirmed his client's decision via text message to the Pioneer Press on Thursday, and he spoke to The Associated Press on Friday.
"He's just tired of litigation and dealing with these issues and having it hanging over him," Ginsberg said.
Williams' choice to stop pursuing the matter clears the way for the NFL to reinstate his four-game suspension in 2011. Williams, 30, is set to make $6 million next season; a suspension would cost him $1.4 million, according to the Pioneer Press.
League spokesman Greg Aiello didn't immediately respond to a request for comment Friday.
The case began in October 2008, when reports emerged that the linemen were among a handful of players who tested positive. The Williamses, who aren't related, weren't accused of taking steroids, and they said they didn't know StarCaps contained bumetanide, a banned diuretic that can mask the presence of steroids.
Pat Williams filed an appeal of the latest ruling to the Minnesota Supreme Court, his agent, Angelo Wright, told the Pioneer Press on Thursday. Ginsberg, who also represents Pat Williams, said Friday that he hopes to have the court's decision within three months.
"He's offended by the NFL and what it's tried to do to him," Ginsberg said. "He's a fighter, and he wants to go out fighting."
By filing the appeal before the 30-day deadline, Williams might be able to avoid a suspension for another season or more.
"We feel this unique case merits further consideration. Therefore, it's in Pat's best interests to pursue this further," Wright told the Pioneer Press. "He understands this is just part of the process."
At 38, Pat Williams was the oldest defensive player in the league last season. He finished a three-year contract with the Vikings and will be a free agent whenever the market opens, an uncertainty given the NFL's labor situation. Ginsberg said Williams plans on playing next season, though the Vikings have been vague on whether or not they'll attempt to re-sign him.
New Orleans Saints defensive end Will Smith and former linemate Charles Grant, currently a free agent, tested positive for the same substance, but they weren't involved in the Minnesota lawsuit. The NFL has held off on enforcing those players' four-game suspensions until the Minnesota case is resolved.
The case was watched by other major sports leagues -- including Major League Baseball, the NBA and the NHL -- which supported the NFL and said their drug-testing programs would be at risk if players were allowed to challenge drug-testing policies in state courts. The NFL has argued its anti-doping policy was a product of its collective bargaining agreement with the players' union and was governed by federal law.
The Associated Press contributed to this report.