Kathleen Folbigg was released from prison on Monday after an inquiry upheld new evidence which cast "reasonable doubt" on her convictions.
Originally accused of smothering her children, the evidence suggested they died due to rare genetic abnormalities.
The 55-year-old said she was "humbled" and "grateful" to be free.
"For the past 20 years I have been in prison, I have forever, and will always, think of my children [and] grieve for my children," she said in a video statement.
Ms Folbigg also thanked her friends and supporters, who in recent years waged a campaign for her case to be reviewed.
"I would not have survived this whole ordeal without them," she said.
Ms Folbigg was met at the prison gates by long-time friend Tracy Chapman, who said she spent her first day of freedom enjoying simple pleasures.
These included a comfortable bed, pizza and garlic bread, and a Kahlua and coke, Ms Chapman told reporters, adding that Ms Folbigg was "in awe" of modern technology such as smartphones.
"There's no hate in Kath's heart, she just wants to live a life she missed for the last 20 years and move on," she said.
Ms Folbigg would now seek to have her convictions quashed in the Court of Criminal Appeal, lawyer Rhanee Rego said.
New South Wales Attorney General Michael Daley said Ms Folbigg had been granted the unconditional pardon due to a recent inquiry into her case.
The inquiry, led by retired judge Tom Bathurst, heard all four children could have died from natural causes.
A team of immunologists found that Ms Folbigg's daughters shared a genetic mutation - called CALM2 G114R - that can cause sudden cardiac death.
Evidence was also uncovered that her sons possessed a different genetic mutation, linked to sudden-onset epilepsy in mice.
-- Courtesy of BBC News
