Barnett, a flight attendant, and Todd, a stockbroker, wed in 1991 in South Carolina, but the marriage quickly crumbled and Barnett filed for divorce while pregnant with Savanna.
A bitter divorce and custody battle ensued, with Todd winning full custody.
In April 1994, Barnett had a supervised visit with Savanna and disappeared, allegedly living in Europe, South Africa and New Zealand before settling in Queensland.
Barnett, who faces a 30-year jail sentence, was extradited from Queensland to the US last week.
US judge Bristow Marchant ordered Barnett, who did not apply for bail, be held in the Charleston County Jail. Todd was not in court to face his former wife.
"He is aware of Lee's return and appreciative of the dedication of the FBI and Department of Justice over the 20-year span since his daughter was kidnapped," Todd's lawyer, Graham Sturgis, told AAP.
"He hopes that this will shed light on the devastating problem of parental kidnappings so that other parents and children won't suffer its tragic effects."
Todd never gave up hope of finding Savanna and continually updated her bedroom so it would be age appropriate for her return.
Sturgis pointed to a US Department of Justice report, The Crime of Family Abduction: A Child's and Parent's Perspective, to show the pain victims of child abduction endure.
- AAP