In a statement released on Wednesday, Corbett said:
"I have thoroughly reviewed Judge Jones' opinion in the Whitewood case. Given the high legal threshold set forth by Judge Jones in this case, the case is extremely unlikely to succeed on appeal. Therefore, after review of the opinion and on the advice of my Commonwealth legal team, I have decided not to appeal Judge Jones' decision.
"As a Roman Catholic, the traditional teaching of my faith has not wavered. I continue to maintain the belief that marriage is between one man and one woman. My duties as Governor require that I follow the laws as interpreted by the Courts and make a judgment as to the likelihood of a successful appeal.
Gov. Tom Corbett's decision Wednesday means that same-sex marriage will remain legal in Pennsylvania, without the threat that a higher court will reinstate the ban.
Pennsylvania is the 19th state to recognize same-sex marriages. Hundreds of gay couples apply for marriage licenses after Jones' ruling Tuesday.
Pennsylvania is the last northeastern U.S. state to legalize gay marriage.
U.S. District Judge John E. Jones III called the plaintiffs - a widow, 11 couples and one couple's teenage daughters - courageous for challenging the constitutionality of the ban passed by lawmakers in 1996.
"We are a better people than what these laws represent, and it is time to discard them into the ash heap of history," the judge wrote.
RELATED: Read Judge Jones' ruling
Corbett's office was left to defend the law after Democratic Attorney General Kathleen Kane refused to do so.
State marriage bans have been falling around the country since the U.S. Supreme Court last year struck down part of the federal Defense of Marriage Act.
The ACLU had argued that the bans deprive same-sex couples and their families of the legal protections, tax benefits and social statuses afforded to married couples.
The Pennsylvania lawsuit, filed July 9, was the first known challenge to the state ban. At least five later test cases emerged, including one over a suburban county's decision last year to issue 174 marriage licenses to same-sex couples, before a court shut them down. Officials in Montgomery County were trying Tuesday to have that order lifted.
Amid a frenzy of celebration across the state, county offices in Philadelphia stayed open late to handle marriage applications, while officials in Pittsburgh were closed for election day but accepting them online. Couples must wait three days before getting married, unless a sympathetic judge grants a waiver.
Joe Parisi told his partner to "jet out of work" and get to Philadelphia City Hall.
"We didn't want to take the chance of having this be challenged and missing out on our opportunity," said Parisi, a Philadelphia resident who plans to marry Steven Seminelli.
They were among the first to get a license Tuesday afternoon, just hours after the judge's ruling.
The judge also ordered Pennsylvania to recognize same-sex marriages performed elsewhere.
Vic Walczak, legal director of the American Civil Liberties Union of Pennsylvania, which pursued the case, said of the ruling: "It's everything we had hoped for."