Mr Edwards said the discovery 126 years after the murders proves beyond doubt that Kosminski - one of the six key suspects commonly cited as the Ripper - was the actual killer.
He said the shawl had been taken by acting Sergeant Amos Simpson, who was on duty the night of Eddowes's death and wanted it for his wife.
But horrified at the blood-soaked wrap, she never wore it, and it was stored away and passed down through the generations until it came to auction seven years ago.
Mr Edwards said: "Thank God the shawl has never been washed, as it held the vital evidence."
The author, who said he was part-inspired to take up the search for the killer after watching the Johnny Depp film From Hell about the Ripper murders, said police had identified Kosminski as a suspect, but never had enough evidence to bring him to trial.
Kosminski was a Polish Jewish immigrant who, fleeing persecution in his Russia-controlled homeland, came with his family to England in 1881 and lived in Mile End Old Town.
He was admitted to a string of lunatic asylums, where he died in 1899 of gangrene in the leg.
Naming Jack the Ripper will be published by Sidgwick & Jackson on Tuesday and costs £16.99 for a hardback.
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