"The jurisprudence of equal protection and substantive due process has undergone what can only be characterized as a sea change since 1972," Jones wrote.
The judge said last month that he saw no reason why the trial could not begin in early to mid-2014.
Attorneys representing the same-sex couples or relatives who have sued to overturn the law said they were delighted that their clients would have their day in court.
"They are married in every sense of word except one - under Pennsylvania law," said Mark Aronchick, a partner with the Philadelphia firm Hangley, Aronchick. "We are asking the state to recognize that."
A Corbett administration spokesman said its lawyers had not decided if they will appeal the ruling.
"We are under obligation to defend the laws of the commonwealth," said Joshua Maus, press secretary for the governor's Office of General Counsel.
The ACLU sued Gov. Corbett and his administration in July on behalf of 23 plaintiffs over the state's 1996 ban, which prohibits same-sex marriage in Pennsylvania and does not recognize such marriages performed elsewhere.
Fifteen states and the District of Columbia now allow same-sex marriage.
The plaintiffs contend that the law violates the equal protection and due process clauses of the 14th Amendment.
Under an agreement, Corbett and Attorney General Kathleen Kane were dropped as defendants in the case and Revenue Secretary Dan Meuser was added as a defendant, along with Health Secretary Michael Wolf. Bucks County Register of Wills Donald Petrille Jr. also remains a defendant.