In a letter to The Sunday Telegraph, he writes: "I ordered their removal. Later, I had them burned. They were a curse and business tripled following their removal."
The warrants – from the Queen; the Duke of Edinburgh; the late Queen Elizabeth, the Queen Mother; and the Prince of Wales – were taken down in 2000.
They had been displayed since the late Queen Elizabeth first gave her approval in 1938.
The Duke had written to the businessman five months earlier to inform him that he would not be renewing his warrant after 40 years because he no longer patronised the shop in Knightsbridge.
He had been accused by Mr Fayed in court of masterminding the deaths of the tycoon's son Dodi and Diana, Princess of Wales, in a car crash in 1997.
In his letter, Mr Fayed, 77, also calls for the store's new owners, who enjoy close links to the British Royal family, to retain the two memorials that he erected to the memory of his son and the late Princess.
This newspaper's Mandrake column reported last weekend that the Qataris were considering their removal.
"Unless and until this country gives the Princess the thanks and devotion she deserves in the form of fitting public memorial, this statue, Innocent Victims, should remain to remind the world of what was lost when two young people, on the brink of happiness together, were killed," he writes.
The tycoon did not say whether he had been given any reassurances by the Qataris about the future of the bronze statue, which was erected in 2005 and depicts the pair raising their hands to a seagull.
He claims, however: "I believe the new owners of Harrods regard it with the same reverence as the thousands who visit it every week."
He adds: "It is the only memorial to the Princess in the country, if one discounts the misconceived municipal water works in Hyde Park that every year causes casualties among the children who slip over when paddling in it."
The second Harrods memorial, which was unveiled in 1998, consists of photographs of the pair behind a pyramid-shaped display that holds a wine glass still smudged with lipstick from the Princess's last dinner, as well as a ring Mr Fayed's son purchased for her the day before they died during a visit to Paris.
Helen Bowman, of English Heritage, said that although Harrods was housed in a listed building, the memorials could legally be removed.
She said: "These are temporary structures, and, as such, were not part of the original assessment of the building's architectural and historic merit. We appreciate, however, that there may be affection for them."
A spokesman for Harrods said no decision about the future of the memorials had been made.
by By Richard Eden / The Telegraph
Published: 7:00AM BST 22 Aug 2010