The couple also endured four inquests and a royal commission.
The ordeal wrecked the Chamberlains' marriage and scarred their children.
Their oldest son Aidan, who was with his parents to hear the inquest's finding, has not coped well.
"He has a lot of anger pent up in him that he is slowly managing to let go," Chamberlain-Creighton said.
"And this [finding] is, you know, a huge way towards helping with that finally."
Even with continuing doubts among many Australians, a wave of support and relief has swept across the nation's newspapers, airwaves and websites.
Broadcaster Wendy Harman apologised on her site after the inquest's emotional conclusion, one of only two apologies Chamberlain-Creighton said she had ever received from the media.
The other was from Channel Ten news director Kevin Hitchcock, in the 1980s.
Chamberlain-Creighton said they, and others who had apologised for believing she had killed Azaria, had shown "a huge amount of courage" in admitting they were wrong.
She said she would appreciate an apology from the Northern Territory Government, but not if it was forced.
The remorse now flooding Australia underscores the depth of feeling and fascination that has surrounded Azaria's tragic disappearance.
Jack Waterford, the Canberra Times' editor-at-large, noted that more than half of the population had no personal memory of the case: they were either not born, or too young.
The Australian's Stuart Rintoul added that in the time it had taken for the Chamberlains to be exonerated, Australia had elected six prime ministers and the population had grown from 14.5 million to almost 23 million.
Newspaper and website readers applauded Tuesday's finding, which most said was long overdue, would allow Azaria to be grieved for as she should have been three decades ago, and gave closure to the Chamberlains.
The sentiment flowed through the media. "Justice at last for tearful Lindy: vindicated," the Herald Sun headlined.
The newspaper also said it was "time to put bad blood to rest", while the Telegraph said that in expressing sympathy for "the death of your dear and loved daughter Azaria" coroner Morris spoke for many Australians.
The Canberra Times was more bitter: "That it took authorities so long to accept that the Chamberlains were right all along will ensure that this case remains a byword for ignorance and injustice in the Northern Territory."
And in the Australian, columnist Errol Simper, who covered the case from the 1982 trial, wrote that the finding said more than the obvious truth that Azaria had not been murdered. "It also said that Azaria's long-suffering parents, Lindy and Michael, are honourable people who'd always told the truth."
