Court documents showed Barnett would be subject to a supervised release term of two years.
Barnett was found guilty of "international parental kidnapping" and making a false statement in an application for a US passport.
After losing custody of her daughter and leaving the United States with Savanna in 1994, Barnett first went to South Africa where she married Juan Geldenhuys, before moving to New Zealand and becoming a citizen.
Barnett lived on the North Shore before moving to Australia in 2007.
Savanna turned 22 this month and was now known as Samantha Geldenhuys. She only learned about her identity and her mother's life on the run after Barnett was arrested in Queensland in late 2013.
Her father, stock broker Benjamin Harris Todd III, was granted sole custody of her when she was a baby.
A criminal docket filed in a South Carolina court alleged Barnett went by the aliases Alexandria Maria Canton, Alexandria Maria Geldenhuys, Lee Barnett Todd and Lee Barnett.
Posts on Facebook and comments Barnett's relatives made to US news outlet ABC4 confirmed she was now out of jail.
According to an affidavit cited on ABC4, Barnett gained New Zealand citizenship in 2008.
A court judgement said Barnett was to have no contact with Mr Todd and was not allowed to own firearms or "any other dangerous weapon."
