The intelligence files describe the 1st Earl Mountbatten of Burma and his wife Edwina as 'persons of extremely low morals' who frequently had extramarital affairs.
One source said Mountbatten's penchant for young men made him 'an unfit man to direct any sort of military operations'.
The files paint a very different picture of the last viceroy of India - who was hailed as a war hero who led allied efforts in southeast Asia before he was assassinated in 1979 by an IRA bomb.
It is not known why agents began compiling the dossier, but the FBI has long been known to keep compromising material on high-profile figures, most famously Martin Luther King.
Comment: The 'compromising' material the FBI claimed to have on MLK was most likely made up in an attempt to smear his name and legacy: JFK files: Dodgy FBI documents allege Martin Luther King Jr. 'had secret lovechild, attended orgies'
The 75-year-old FBI documents were obtained through a freedom of information request by British historian Andrew Lownie, who has written a biography of the couple.
In the book, The Mountbattens: their Lives & Loves, Mountbatten's former driver Ron Perks reveals that one of his boss's favourite destinations was 'an upmarket gay brothel used by senior naval officers' called the Red House near Rabat.
Agents began compiling the file, which spans more than three decades, in February 1944, shortly after Mountbatten became supreme allied commander of southeast Asia.
Following his appointment, the FBI interviewed Elizabeth de la Poer Beresford, Baroness Decies, about another matter, and she brought up Mountbatten, The Sunday Times reports.
The file reads: 'She states that in these circles Lord Louis Mountbatten and his wife are considered persons of extremely low morals.
'She stated that Lord Louis Mountbatten was known to be a homosexual with a perversion for young boys.
'In Lady Decies' opinion he is an unfit man to direct any sort of military operations because of this condition. She stated further that his wife Lady Mountbatten was considered equally erratic.'
It was signed EE Conroy, head of the New York field office, who wrote that she 'appears to have no special motive in making the above statements'.
Agents opened more files on Mountbatten after World War II when he became Nato commander of allied forces in the Mediterranean, then admiral of the fleet, and later chief of the defence staff.
But the FBI's interest in Mountbatten peaked around the Suez crisis, with the Bureau opening files in November 1955 and November 1956.
Rumours about Mountbatten's sexuality have long swirled following his death 40 years ago.
The royal kept a large group of gay friends, including Noël Coward, Terence Rattigan, Ivor Novello and Tom Driberg, who reportedly referred to him as 'Mountbottom'.
Lownie's new book, to be published on Thursday, contains an interview with Anthony Daly, a rent boy to the rich and famous during the 1970s.
Daly claims: 'Tom said Mountbatten had something of a fetish for uniforms — handsome young men in military uniforms (with high boots) and beautiful boys in school uniform.'
Comment: The more pressing issue here is whether Lord Mountbatten is yet another elite figure who was also an abuser of children. There are statements that support this fact but, as it is, while he may have had "low morals" and could have been an ideal target for blackmail - an undesirable quality for someone in his position - more data is needed. The timing of this release is also interesting considering the accusations against Prince Andrew and his connections with convicted, now dead, pedophile Epstein. It's also notable that similar rumours surround his nephew, Prince Charles, partly because of his friendship with known pedophiles: