A unanimous Victorian County Court jury in December found Pope Francis' former finance minister guilty of molesting two 13-year-old choirboys in Melbourne's St Patrick's Cathedral in the late 1990s shortly after Pell became archbishop of Australia's second-largest city.
Today's decision comes as the father of one of the two boys Pell molested — a victim who died aged 31 over an accidental heroin overdose — wrote a letter to the Vatican demanding answers to seven crucial questions.
Among the questions in the letter, sent to news.com.au, was the question: "Why has Pell kept his title as cardinal?"
The Vatican has repeatedly refused to comment on the case before Pell had exhausted all of his legal avenues for appeal.
The Victoria Court of Appeal in August rejected Pell's appeal in a 2-1 ruling.
Pell was sentenced to six years in prison in March and is no longer a member of Francis' Council of Cardinals or a Vatican official.
Pell's lawyers argued in their 12-page application for a High Court appeal that two state appeals court judges made two errors in dismissing his appeal in August.
The judges made a mistake by requiring Pell to prove the offending was impossible rather than putting the onus of proof on prosecutors, the lawyers said.
They also said the two judges made a mistake in finding the jury's guilty verdicts were reasonable.
Pell's lawyers argued there was reasonable doubt about whether opportunity existed for the crimes to have occurred.
Pell's lawyers also argue that changes in law over the years since the crimes were alleged have increased the difficulty in testing sexual assault allegations.
They argue Pell should be acquitted of all charges for several reasons, including inconsistencies in the complainant's version of events. But prosecutors argue there is no basis for the appeal, and the Victorian courts made no errors.
In their written submission to the High Court, prosecutors wrote Pell's legal team was asking High Court judges to apply established principles to the facts of the case, which were already carefully and thoroughly explored by the state appeals court.
Pell was largely convicted on the testimony of one victim. The second victim died of an accidental heroin overdose in 2014 when he was 31 without complaining that he had been abused.
The surviving victim said after Pell lost his appeal in August, "I just hope that it's all over now."
Clerical sexual abuse and the Catholic Church's handling of such cases worldwide have thrown Francis' papacy into turmoil.
In a little more than a year, the Pope has acknowledged he made "grave errors" in Chile's worst cover-up, Pell was convicted of abuse, a French cardinal was convicted of failing to report a paedophile, and a third cardinal, former US church leader Theodore McCarrick, was defrocked after a Vatican investigation determined he molested children and adults.
Pell must serve at least three years and eight months behind bars before he becomes eligible for parole.
As a convicted paedophile, he is provided with extra protection from other inmates and spends 23 hours a day in solitary confinement.
