HOUSTON — The prison sentence of Jeffrey Skilling, the former Enron chief executive who spearheaded the pervasive fraud that destroyed the energy company, was reduced by 10 years on Friday after a federal judge approved a deal between his lawyers and prosecutors.

U.S. District Court Judge Simeon T. Lake III, who oversaw Skilling’s trial in 2006, signed off on an agreement that will decrease his 24-year sentence to 14 years. The reduction was driven in part by a 2009 appeals court ruling that ordered a recalculation of Skilling’s sentence because of a mistake made by the judge in interpreting the federal sentencing guidelines.

Skilling, 59, who has been serving his sentence at a federal prison in Jefferson County, appeared in court Friday wearing a khaki-colored prison uniform and a salt-and-pepper beard.

He now is to exit prison as early as 2017, with the standard 15 percent sentence reduction for good behavior and a one-year reduction for completing a substance-abuse treatment program.

“We are relieved that Jeff can now look forward to a day when he can come home to his family and friends,” Skilling’s lead lawyer Daniel M. Petrocelli said.

In exchange for his reduced sentence, Skilling gave up about $42 million, all of which will be distributed to victims of Enron’s fraud. He also agreed not to pursue any further legal appeals, including a claim that would have accused the prosecution team of withholding exculpatory evidence.