The lawsuit, filed on November 9, alleged inconsistent treatment by county election officials of mail-in ballots.
Some counties notified voters that they could fix minor defects such as missing “secrecy envelopes” while others did not.
The lawsuit also initially alleged that Republican observers were denied access to the counting of mail-in ballots, an assertion election officials dispute. The campaign on November 15 dropped claims relating to those allegations, but later asked to add them.
Judge Brann had expressed scepticism of the lawsuit at a hearing on Tuesday.
Pennsylvania officials can certify election results that currently show Mr Biden winning the state by more than 80,000 votes, the federal judge ruled on Saturday.
“In the United States of America, this cannot justify the disenfranchisement of a single voter, let alone all the voters of its sixth most populated state,” the judge said. “Our people, laws, and institutions demand more.”
Mr Trump’s team had argued that the US Constitution’s guarantee of equal protection under the law was violated when Pennsylvania counties took different approaches to notifying voters before the election about technical problems with their submitted mail-in ballots.