Hatch, 45, of Newport, R.I., was convicted by a federal jury in January of failing to pay taxes on the prize and other income. He was sentenced in May to 51 months in prison by a judge who said the reality TV star had repeatedly lied on the witness stand.
He arrived at the minimum-security facility in Morgantown on July 25.
Hatch, who became known as the "fat naked guy" for refusing to wear clothes on the CBS show, is now required to wear khaki shirts and pants.
"I'm doing lots of intake stuff, like clothing and getting to know the place ... but I don't think I will adjust to any of this until I can prove I was unethically prosecuted," he told The Dominion Post of Morgantown during a phone interview Wednesday.
Hatch said he will be tutoring inmates, helping them to earn their GEDs and hone their job-hunting skills.
"Sure, people know my name ... there are 1,300-plus inmates who think they know me, so it's an interesting experience," he said. "They all have questions — want to know what this experience is like and what 'Survivor' was about."
While his lawyer works on his appeal, Hatch said he is using his time to read and write a book about his experiences on "Survivor" and his subsequent legal problems.
"I'm focused on writing what has gone so terribly wrong," he said.