The 230-year-old unknown mummy was discovered four decades ago during excavations of Barfusser church in Basel.
Johnson has not publicly commented on the new certainty about his heritage, and it is unclear if his DNA was used to discover matches with that found on the mummy's big toe.
With a 99.8 per cent probability that the descendants and the mummy were all from the same maternal line, the scientists and historians were confident that the mummy is Anna Catharina Bischoff.
Initial testing of her wooden coffin suggested it dated from the 16th Century, yet these clues alone were not enough.
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Once her identity had been established, genealogists were able - with the help of the efficient records of births, marriages, and deaths which tend to be kept by the wealthier classes - to trace more of Anna Catharina's descendants.
Her daughter married Christian Friedrich Pfeffel von Kriegelstein, Dr Hotz said, making her an ancestor of Mr Johnson, whose full name is Alexander Boris de Pfeffel Johnson. She is believed to be Johnson's great-great-great-great-great-great-great grandmother, according to researchers who had been testing her body since 2015and announced their findings on Thursday.
Once Anna Catharina's husband passed away, she returned to her hometown and started an intense treatment to cure the disease, but to no avail.
Five generations of von Pfeffels later, Marie Luise von Pfeffel marryied Stanley Fred Williams.
Johnson once told the genealogy series Who Do You Think You Are that he was "the product of many countries" - and that he thought he was part Jewish, part French, part English, part American and part Turkish.
It did not work: scientists believe Anna Catharina probably died from mercury poisoning.