The mummy was found decades ago at Barfuesser Church in Basel but her identity at that stage was a mystery.
They then extracted DNA from the mummy's toe which gave a 99.8% match to two living descendants - living in Basel and Ohio, Dr Hotz said.
Local historians knew that members of Basel's wealthy families were buried in and around the Barfüsser Church.
Anthropologist Gerhard Hotz, curator at Basel's Natural History Museum, said identifying her took two years of thorough research, having started with nearly no information on who the mummy was.
Image: The mercury that killed Bischoff is likely responsible for her preservation.
Initial testing of her wooden coffin suggested it dated from the 16th Century, yet these clues alone were not enough.
The pastor's daughter, aged 67 when she died, had seven children one of whom married a Baron Pfeffel of Kriegelstein, a member of Johnson's family tree, the Swiss news agency SDA reported.
Five generations of von Pfeffels later, and Marie Luise von Pfeffel married Stanley Fred Williams.
SRF The mummy has been identified as Anna Catharina Bischoff
It was there that she contracted syphilis, while caring for patients affected by the disease.
He previously told the BBC programme Who Do You Think You Are? that he was a "product of many countries" and described his von Pfeffel ancestors as "posh toffs".
On the death of her husband she returned to her home town of Basel, and apparently underwent rigorous mercury treatment in the hope of a cure.
But following several years of research, scientists have now revealed that the best preserved mummified remains in Switzerland are those of Anna Catherina Bischoff.
Ms Bischoff died in Basel in 1787 aged 68.
But the mercury also preserved her body - allowing today's researchers to find out exactly who she was, and who her descendants are.
Johnson is related to Anna Bischoff through the lineage of his father, Stanley Johnson, according to the BBC.