The emotional video statement follows the end of Folbigg's 20-year stint behind bars after she was convicted over the deaths of her four young children.
New scientific evidence submitted to a second inquiry into her convictions ultimately led to Folbigg being unconditionally pardoned and released from the Clarence Correctional Centre in Grafton on Monday.
She is now staying with long-time friend and supporter Tracy Chapman on her farm on the NSW mid-north coast.
Ms Folbigg celebrated her release as "a victory for science" in the video message released on Tuesday.
"I'm extremely humbled and extremely grateful for being pardoned and released from prison," she said.
"My eternal gratitude goes to my friends and family, especially Tracy and all of her family, and I would not have survived this whole ordeal without them.
"Today is a victory for science and especially truth.
"For the last 20 years I have been in prison, I have forever and will always think of my children, grieve for my children and I miss them and love them terribly."
Folbigg was jailed in 2003 after a jury found her guilty of three counts of murder and one of manslaughter over the deaths of her young children, Caleb, Patrick, Sarah and Laura, between 1989 and 1999.
She was sentenced to 40 years in prison. The term was later reduced on appeal to 30 years, with a minimum of 25.
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