The musician was chosen to a receive an Officer of the Most Excellent Order of the British Empire (Obe) medal in the Queen's New Years Honours List in 2000, but Harrison refused the honour.
The snub was revealed in paperwork obtained by Britain's Mail on Sunday newspaper.
Harrison previously accepted a Member of the Most Excellent Order of the British Empire (Mbe) medal from the royal in 1965 along with his Beatles bandmates, although John Lennon later sent his back as part of a peace protest.
Reports suggest Harrison snubbed the Obe honour because he would have preferred a knighthood, an award which was handed to his bandmate Sir Paul MCCartney in 1997.
The star died in 2001, just a year after he turned down the Obe.