A 9-week-old baby disappeared from a campsite near Ayers Rock, a desert landmark in northern Australia. Michael and Lindy Chamberlain said a dingo had snatched the child.
Tuesday's announcement marked the end of the fourth and final inquest in the case that divided Australians and inspired a 1988 film starring Meryl Streep.
"We're relieved and delighted to come to the end of this saga," a tearful but smiling Lindy Chamberlain-Creighton, since divorced and remarried, told reporters outside the court.
The first inquest in 1981 had also blamed a dingo. But a second inquest a year later charged Chamberlain-Creighton with murder and her husband with being an accessory after the fact. She was convicted and served more than three years in prison before that decision was overturned. A third inquest in 1995 left the cause of death open.
"The dingo has done it. I'm absolutely thrilled to bits," said Yvonne Cain, one of the 12 jurors in the 1982 trial that convicted a then-pregnant Chamberlain-Creighton of murder. "I'd always had my doubts and have become certain she's innocent."
Cain said she still encounters people who doubt the couple's innocence, but they inevitably misunderstand what evidence there was against them.
"When people say she's guilty, I say: `You have no idea what they're talking about - I was there,"' she said.
The case became famous internationally through the 1988 movie "A Cry in the Dark," in which Streep played the mother.
Many Australians initially did not believe that a dingo was strong enough to take away the baby, whose body has never been recovered. Public opinion swayed harshly against the couple; some even spat on Chamberlain-Creighton and howled like dingoes outside her house.
No similar dingo attack had been documented at the time, but in recent years the wild dogs native to Australia have been blamed for three fatal attacks on children. Few doubt the couple's story today, but the latest inquest - which the family had fought to get - made it official that Azaria was killed in a dingo attack.
But not all Australians accept the latest ruling.
A policeman who was at Uluru the night Azaria disappeared said he still believes the first coroner's finding that there was some human intervention.
Frank Morris, who has since retired from the police force, said while he was not trying to blame the parents, he thought someone played a part in moving clothing Azaria wore that night.
"We don't know who. That is the $64,000 question," Morris said.
"If you go to court enough times, you are bound to get a win sooner or later," Morris added of the parents' victory Tuesday.
The findings mirror those of the first coroner's inquest in 1981. But that inquest found that somebody had later interfered with Azaria's clothing, which was later found relatively unscathed in the desert.
A second coroner's inquest triggered a Northern Territory Supreme Court trial that resulted in Chamberlain-Creighton being found guilty of slashing her daughter's throat and making it look like a dingo attack.
She was convicted in 1982 and sentenced to life in prison with hard labor.
She was released in 1986 after evidence was found that backed up her version of events: the baby's jacket, found near a dingo den, which helped explain the condition of the rest of the baby's clothing. A Royal Commission, the highest form of investigation in Australia, debunked much of the forensic evidence used at her trial and her conviction was overturned.
A third inquest could not determine the cause of death.
The fourth inquest heard new evidence of dingo attacks, including three fatal attacks on children since the third inquest.
The Associated Press contributed to this report.