"Free, fair elections are the lifeblood of our democracy. Charges of unfairness are serious. But calling an election unfair does not make it so," wrote Stephanos Bibas on behalf of a three-judge panel.
"Charges require specific allegations and then proof. We have neither here," wrote Bibas, who was nominated by Trump.
The Trump campaign and its supporters have tried and failed to convince judges of election irregularities in Michigan, Georgia, Arizona and Nevada, all critical to Biden's victory.
"Voters, not lawyers, choose the President. Ballots, not briefs, decide elections," said the appeals court opinion.
"On to SCOTUS!" wrote Jenna Ellis, a Trump campaign attorney, on Twitter after the ruling, referring to a planned appeal to the U.S. Supreme Court. "The activist judicial machinery in Pennsylvania continues to cover up the allegations of massive fraud."