"Listen to yourself you filthy, abnormal animal," the letter reads.
"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."
When King received the letter, he told friends that someone wanted him to kill himself, the Times reported.
The letter goes on to tell King: "There is only one thing left for you to do. You know what it is" - an apparent exhortation for him to kill himself.
The letter was crafted to make it appear it came from someone within the civil rights movement, making a reference to "us Negroes".
"You could not believe in God and act as you do," the letter states.
"Clearly you don't believe in any personal moral principles."
The document provides a compelling illustration of how deeply paranoid the FBI had become under the stewardship of Hoover, whose name still adorns the federal police agency's Washington headquarters.
Hoover believed King was being influenced by communists, and King accused the FBI of failures in stopping violence against blacks in the segregated Deep South.
In 1963, King famously made his "I Have a Dream" speech in Washington during an enormous rally in the nation's capital.
The march helped set the stage for the Civil Rights Act of 1964 that outlawed major forms of racial discrimination, followed a year later by the Voting Rights Act, designed to guarantee the franchise for all black US citizens.
King was gunned down by a sniper in 1968.
-AAP