Her father, Rian Roberts, who had virtually given up hope of finding her alive, yesterday called her survival "amazing".
Ms Roberts (28) was discovered near Haast on Tuesday evening in "remarkably good shape", after last being seen at Fox Glacier on January 3.
Two tourists, a French man and a Swedish woman who were out for a run, recognised her car about 6pm on Tuesday from posters plastered around the West Coast by her brothers and alerted police.
The car was stuck about 300m down a track.
Senior Constable Robin Manera was examining the car when he heard Ms Roberts calling out from nearby dense bush.
Volunteer firefighters and St John members from Haast helped police cut a 100m track to Ms Roberts so she could be carried out.
"I am so glad I have been found," she told Const Manera. "Can you please let my parents know?"
Mr Roberts, who spent four hours with her on Tuesday night, said she was in great spirits and had plenty to say.
However, she had infected feet from mosquito bites, was initially unable to walk and was just "skin and bones".
She had eaten some strawberries on January 3 and had then had nothing more to eat until she was rescued.
Ms Roberts had survived by drinking water from pools in the swampy area.
She said she had started shaking uncontrollably two days before she was found.
She found she was unable to drink water, so she drenched her T-shirt in water and sucked on that.
Ms Roberts had left a family gathering in Cromwell on January 3 in an agitated state after a medication change on Christmas Eve.
After she got stuck on the West Coast track, she stayed with the car for two days before wandering into the bush.
"People have this stigma about mental illness," Mr Roberts said. "But there's a lot of people who don't have mental illness who wouldn't have survived this.
"She's definitely my hero."
Mr Roberts believes prayers from family and friends helped keep his daughter alive.
He and family and friends had worked hard to make sure every avenue in the search was covered, including producing and distributing hundreds of posters.
He wanted to send "heartfelt thanks" to all those involved in the searches and also those who helped his family get through each day.
Ms Roberts was yesterday transferred from Dunstan Hospital, Clyde, to Dunedin Hospital.
A Dunedin Hospital spokesman said last night she was being assessed.
