The case has garnered broad attention both for its secrecy and for the precedent it set. Abuse survivors had hailed the conviction as proof that judicial systems can hold even the most senior prelates accountable in the global child sexual abuse scandal that has stained the church’s image.

Cardinal Pell, wearing a black suit with a clerical collar, hung his head when the ruling was announced in a packed courtroom, where victims of childhood sexual abuse were present.

In a news conference after the judgment was issued, Vivian Waller, a lawyer for one of the former choirboys, read a statement on his behalf in which he expressed relief and the hope that this decision signaled the end of the criminal process.

“The journey has taken me to places that in my darkest moments I feared I would not return from,” the statement read. “I just hope that it is all over now.”

Experts said that the new ruling could be challenged in the High Court of Australia, the nation’s top court.

The cardinal, who has been imprisoned since his sentencing in March, began his appeals process in June. The primary argument made by Cardinal Pell’s legal team was that it was impossible for the jury to be satisfied of the cardinal’s guilt “beyond reasonable doubt.” The lawyers pointed to what they said was evidence that contradicted the account of the former choirboy — testimony that the case hinged on.

“Nobody apart from the alleged victims and the alleged perpetrator were present in the room,” said Bret Walker, the lawyer representing Cardinal Pell at the appeal. Activities after the Sunday Mass, Mr. Walker added, would have made it either “impossible” or “so unlikely” as to leave no realistic possibility for Cardinal Pell to molest them.

But two of the three judges said Wednesday that the standard had been met for the jury to determine the cardinal’s guilt beyond reasonable doubt.

“We did not experience a doubt,” Justice Ferguson said. “The complainant was a very compelling witness, was clearly not a liar, was not a fantasist and was a witness of truth,” she added.

Justice Mark Weinberg dissented, finding that “the complainant was inclined to embellish aspects of his account.”

The defense had also appealed the verdict on two other, more technical grounds: the trial judge’s refusal to permit a video presentation during the defense’s closing arguments, and the fact that Cardinal Pell was not arraigned in the presence of the jury. All three judges declined to overturn the cardinal’s conviction on those grounds.

The Australian judiciary differs from that of the United States in giving appeal courts broad discretion to overturn decisions made by juries.

“The idea is that to safely convict someone, you have to convince the jury and the appeal board,” said Jeremy Gans, a law professor at the University of Melbourne. The judges in Cardinal Pell’s case, he added, did not have a track record of ruling jury judgments unreasonable.

While the Vatican expelled Cardinal Pell from a powerful council of papal advisers in December, it has yet to defrock him. A Vatican spokesman said earlier this year that the church would await the resolution of the appeals process before considering further action.

Prime Minister Scott Morrison said on Wednesday that the cardinal would be stripped of his Order of Australia, an award bestowed on Australians who have demonstrated outstanding service or exceptional achievement.

The trial — which ran for almost five weeks last year, and was preceded by a first trial that ended in a hung jury — rested on the testimony of the single former choirboy. He said that after the Sunday Mass in 1996, Cardinal Pell caught him and another boy in the priest’s sacristy, where he molested the boys and forced his erect penis into the complainant’s mouth.

The second former choirboy, who died in 2014, never made any complaint about abuse to his family or the police. When his mother approached him with suspicions that he had been abused, he denied it had happened.

Lisa Flynn, a lawyer who is representing the father of the deceased former choirboy in a separate civil case, said she had found the defense’s arguments worrisome.

“Some of the things that have been said flies in the face of a lot of the findings of the royal commission and what we know about abuse survivors,” Ms. Flynn said, referring to an investigation of institutional child abuse in Victoria conducted in recent years. “In many cases,” she added, “people take their stories to the grave.”

Outside the courtroom, people who said they were survivors of abuse held signs condemning the cardinal and said they were thrilled with the outcome.

“I’m actually beside myself; I expected Cardinal Pell to walk out of this court a free man today,” said one, Vladimir Selakovic. “It gives the victims a hope,” he added. “No one is above the law.”

Cathy Kezelman, the president of the Blue Knot Foundation, an Australian organization that supports people who have experienced trauma, said that “for a long, long time, survivors have not been believed.”

“To have to prove that you suffered so profoundly is really incredibly challenging,” she added.

During the appeals process, Cardinal Pell appears to have reflected on what he called his own suffering.

His supporters posted a letter online they claimed he had sent from prison. “The knowledge that my small suffering can be used for good purposes through being joined to Jesus’s suffering gives me purpose and direction,” the letter read.