Using deliberate misspellings and awkward constructions, it reads: "Lend your sexually psychotic ear to the enclosure. You will find on the record for all time your filthy, dirty, evil companions, male and females giving expression with you to your hidious [sic] abnormalities.
"It is all there on the record, your sexual orgies. Listen to yourself you filthy, abnormal animal.
"You have been on the record - all your adulterous acts, your sexual orgies extending far into the past. This one is but a tiny sample."
It adds: "King, you are done."
The letter concludes by apparently urging King to take his own life within 34 days - thought to be a reference to the date on which he was to be presented with the Nobel Peace Prize.
"There is but one way out for you. You better take it before your filthy, abnormal fraudulent self is bared to the nation."
In the event, the letter was opened by King's wife, Coretta, and he did not read it until his return from Sweden.
A 1976 Senate hearing into underhand campaigns conducted by the FBI and other intelligence agencies concluded that the letter "clearly implied that suicide would be a suitable course of action for Dr King".
The note was part of a personal vendetta by Hoover against King, after the pastor accused the FBI of failing to protect black people in the Deep South.
In an article about her find in the New York Times Magazine, Gage said: "One oddity of Hoover's campaign against King is that it mostly flopped, and the FBI never succeeded in seriously damaging King's public image.
"Half a century later, we look upon King as a model of moral courage and human dignity. Hoover, by contrast, has become almost universally reviled."