Kathleen Folbigg says she is "extremely humbled" and "extremely grateful" for being pardoned, in her first statement since being released from prison.
"My eternal gratitude goes to my friends and family, especially Tracy [Chapman] and all of her family, and I would not have survived this whole ordeal without them," she said in a video message, released on Tuesday.
She called her release a major victory for "science and truth".
"For the last 20 years I have been in prison I have forever and always, think of my children, grieve for my children, and miss them and love them terribly."
It comes after Ms Chapman, her best friend, said Ms Folbigg had "no hate" in her heart at a press conference, a day after greeting her upon release.
Ms Folbigg, 55, spent her first day of freedom since 2003 enjoying simple pleasures, like a comfortable bed, pizza, metal spoons and a Kahlua and Coke, Ms Chapman said on Tuesday.
"I can't actually say more than, it was a surreal day," she said.
"We just kind of … enjoyed each other's company. She spent a lot of time with my dogs and getting to know my animals."
Ms Chapman said Kathleen has been in "awe" observing smartphones, and digital streaming devices.
On Monday, NSW Attorney-General Michael Daley announced an unconditional pardon had been granted after he received an advanced report on an inquiry into Ms Folbigg's convictions.
The Special Commission of Inquiry, before retired chief justice Tom Bathurst KC, had heard new genetic evidence raised "reasonable doubt" over the mother-of-four's guilt.
Ms Folbigg was convicted for killing all four of her children between 1989 and 1999, with prosecutors alleging she smothered the infants.
She always maintained her innocence and had been unsuccessful in clearing her name through two appeals and a previous inquiry in 2019.
The pardon means she will not have to serve any more time of her minimum 25-year prison sentence.
Ms Folbigg is already back living with Ms Chapman, near the northern NSW town of Coffs Harbour.
News outlets broadcast footage of the two embracing at a rural property, and Ms Folbigg making a cup of tea.
"Oh my God," Ms Folbigg could be heard saying while hugging Ms Chapman.
Former ABC journalist Brigid Glanville, who now works for a PR firm involved in the campaign to free Ms Folbigg, shared a picture of the two friends this morning.
"Tracy Chapman never gave up on her friend Kathleen Folbigg," she wrote on Twitter.
"This picture taken moments after [two] best friends were reunited."
Lawyer, Rhanee Rego, said today the next step was to have Ms Folbigg's convictions quashed in the Court of Criminal Appeal.
That could either happen via a reference from Mr Bathurst, NSW Governor Margaret Beazley or, "failing that", a direct application to the court, she said.
"And we urge everyone to give her privacy while she enjoys the first bit of freedom, and also she'll be honouring the memory of her children as she's done every day for 24 years."
Ms Rego said her client was grateful and held "no hatred" over her treatment, but described the ordeal she had faced as "unimaginable".
"If Australia really wants to make some good from a tragic story, they'll seriously consider reviewing the system of post-conviction review, the same system that took too long to get to today."
Her legal team would decide on what type of compensation she should seek, Ms Rego said.
Ms Chapman said her best friend was focused on enjoying her freedom.
The long-time supporter was "disappointed" by comments released by the lawyer of Ms Folbigg's ex-husband, Craig Folbigg, who still believes she is guilty.
Ms Folbigg "probably won't speak to him", Ms Chapman says.
"There's no hate in Kath's heart. She just wants to live a life she has missed for 20 years and move on."
Danny Eid, the lawyer for Mr Folbigg, said the news has increased the pain and suffering his client had endured for two decades.
"Craig respects the legal processes that have taken place in the trials that Ms Folbigg has faced," Mr Eid said.
"No one person can point and say that the state of New South Wales or the prosecution, the police or otherwise, have failed her, because all of the available material that was presented was done so in a fair manner and decisions were made."
He said Mr Folbigg wanted to celebrate the life of his children, rather than focus on their death.
"The Honorable Mr Bathurst has come to that conclusion along with the inquiry itself, however, it would be interesting to see whether a jury, faced with the same information, would come to the same conclusion."
Earlier on Tuesday, Spanish scientist Carola Vinuesa told ABC Breakfast that Ms Folbigg's release was "very special".
Professor Vinuesa's research was key in discovering the CALM2 gene mutation now believed to have been a reasonable cause of death of the two Folbigg girls, Sarah and Laura.
"As a scientist, you don't always get to do things that really make a difference in someone's life," Professor Vinuesa said.
"And it wasn't just for Kathleen's life, it was really, you know, a celebration of science."
The senior group leader at London's Francis Crick Institute said the research heard at the recent Folbigg inquiry could benefit similar cases around the world.
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