Tages-Anzeiger said the recipient of invalidity benefit, who fled to Thailand in 2011 to avoid incarceration, had agreed to be returned home.
The sex offender had been sentenced to six years by a St Gallen court on multiple counts of rape, incent and sexual assault.
He was arrested in January and is now in a Thai jail awaiting deportation.
The paper quoted Federal Office of Justice spokesman Folco Galli as saying that the Thai authorities had approved the Swiss extradition request.
Since the end of February the extradition decision was “legally valid and enforceable”.
The spokesman said that for security reasons the deportation would only be announced once the convicted child molester had been extradited.
“The form of transportation will take account of his poor state of health,” the paper quoted Galli as saying.
The man is obese, suffering from a metabolic disease.
According to Joe Keel, head of the St Gallen prison office, the convicted criminal’s return flight has already been booked.
Two police officers and one ‘medically trained person’ would be sent from Switzerland to the airport in Bangkok to collect him.