However due to a court backlog, his appeal at the Court of Criminal Appeal could take several months to be processed.
In the meantime, O'Brien is a free man, despite pleading guilty to and being convicted of a litany of horrific abuse against his daughter.
Ellen O'Malley Dunlop, of the Rape Crisis Centre, said the process must be "fast-tracked".
"I truly hope we are not facing a situation where this convicted criminal remains outside of prison for months on end.
"It is up to the DPP and she must prioritise and fast-track this. It needs to happen very quickly for the victim's sake," she said. Judge Paul Carney sparked disbelief after granting O'BFastrien bail, despite describing his crime as "one of the most serious cases of serial rape of a daughter".
The evil pensioner was handed a 12-year sentence for the rape of his daughter Fiona over nine years.
However members of the victim's family broke down in tears when the judge announced that nine years of the sentence was being suspended and that O'Brien was being granted bail.
The decision to allow the sex beast to walk free sparked outrage and reignited demands for tougher sentences for sex crimes.
The fact that O'Brien was granted bail left his daughter Fiona devastated.
Fiona, who bravely waived her right to anonymity, said there "isn't a word in the English language to describe that man and what he did to me".
"It finally dawned on me, the man who admitted raping me for 10 years ... he gets to go back to the comfort of his home. It's utterly heartbreaking.
"From the age of eight I was called my father's whore. Those words will continue to ring in my head for the rest of my life, and so will today," she said.
Neighbours in Old Court Avenue in Bray where Paddy O'Brien lives with his wife Bridget today reacted with shock.
"I was sick to my stomach when I heard about Paddy O'Brien and what he did to his daughter. I was sick that there were kids running around here and we never knew what he was capable of," said one man.
"We don't want him around here. He's evil," he added.
"I've been here for 14 years and am rearing three kids on this road, and I swear I can't believe what this man has done. We are all in absolute shock," the man told the Herald.
The neighbour was also critical of the sentence that was handed down to O'Brien.
"I don't know what these judges are thinking. That man should be locked up for good for what he did to his girl," he said.
O'Brien first raped his victim the night before her Holy Communion and continued his sickening reign of abuse for nine years.
During that period, he raped his daughter in a graveyard, on a beach and in a bedroom.
Although Judge Carney described the serial rapes as "heinous crimes", he suspended three quarters of the sentence because of O'Brien's health
Barrister Paul Anthony McDermott described the court's decision to grant bail as "very very unusual".
"What happened in this case was unusual because normally you get bail before you're convicted and it's based on the idea that you're presumed innocent.
"It's very, very unusual to give someone bail before any appeal in the court of criminal appeal."
The court heard yesterday that O'Brien suffered from arthritis and a heart condition. He is oxygen-dependent at night.
However, the Irish Prison Service told the Central Criminal Court yesterday that they were confident they could treat and manage O'Brien's ailments.
The head of Nursing Services with the Irish Prison Service, Frances Nangle O'Connor, said treatment in prison is as good as that in the community.