The song, which catapulted the singer to fame in 1972, was rumored to be about one of her ex-boyfriends, who include Hollywood legend Warren Beatty and rocker Sir Mick Jagger, but she had persistently refused to name the man behind the track.
But Simon has now revealed who was so vain by giving fans a cryptic clue in an acoustic version of the song, which features on her upcoming album "Never Been Gone."
She tells Uncut magazine, "You know what, I'm just going to tell you this. The answer is on the new version of 'You're So Vain,' on my new record 'Never Been Gone.' There's a little whisper and it's the answer to the puzzle."
The singer whispers Geffen's name backwards in the track, according to Britain's The Sun newspaper.
Geffen ran Simon's Elektra Records label at the time of the song's release and instead of being about a failed relationship, the lyrics are now thought to hint at the singer's lingering resentment after Geffen allegedly put more effort into promoting rival star Joni Mitchell.