His task was to carry out experiments to discover by what method of genetic quirk twins were produced - and then to artificially increase the Aryan birthrate for his master, Adolf Hitler.
Now, a historian claims, Mengele's notorious experiments may have borne fruit.
For years scientists have failed to discover why as many as one in five pregnancies in a small Brazilian town have resulted in twins - most of them blond haired and blue eyed.
But residents of Candido Godoi now claim that Mengele made repeated visits there in the early 1960s, posing at first as a vet but then offering medical treatment to the women of the town.
Shuttling between Argentina, Paraguay and Brazil, he managed to evade justice before his death in 1979, but his dreams of a Nazi master race appeared unfulfilled.
In a new book, Mengele: the Angel of Death in South America, the Argentine historian Jorge Camarasa, a specialist in the post-war Nazi flight to South America, has painstakingly pieced together the Nazi doctor's mysterious later years.
After speaking to the townspeople of Candido Godoi, he is convinced that Mengele continued his genetic experiments with twins - with startling results.
He reveals how, after working with cattle farmers in Argentina to increase their stock, Mengele fled the country after fellow Nazi, Adolf Eichmann, was kidnapped by Israeli agents.
He claims that Mengele found refuge in the German enclave of Colonias Unidas, Paraguay, and from there, in 1963, began to make regular trips to another predominantly German community just over the border in Brazil - the farming community of Candido Godoi.
And, Mr Camaras claims, it was here that soon after the birthrate of twins began to spiral.
"I think Candido Godoi may have been Mengele's laboratory, where he finally managed to fulfil his dreams of creating a master race of blond haired, blue eyed Aryans," he said.
