The Egyptian-born tycoon acquired the business in Knightsbridge following a £615m takeover in 1985.
Ken Costa, an adviser to the deal with Qatar Holdings, said Mr Al Fayed was retiring "to spend more time with his children and grandchildren".
He will continue to promote the store in the role of honorary chairman.
But Mr Al Fayed will not be involved in running the company on a day-to-day basis.
The sale, signed in the early hours of 8 May, will include all parts of the Harrods group, including Harrods Estates and a charter aircraft service.
Qatar Holdings is the investment arm of the emirate's sovereign wealth fund, Qatar Investment Authority.
Although it failed in a bid for Sainsbury's in 2007, it is the third-largest shareholder in car-maker VW and has a stake in Porsche. It also bankrolled Barclay's Bank during the banking crisis, enabling Barclay's to avoid going to the government for financial help.
Its chairman, Sheikh Hamad Bin Jassim Bin Jabr Al-Thani, who is also Qatar's prime minister, said Harrods would add "much value" to its portfolio of investments and generate "good and stable returns as a business".
He added: "It's a historical place. I know it's important, not only for the British people but it is important for the tourism."
His vice-chairman, Dr Hussain Ali Al-Abdulla, said the acquisition was a "landmark transaction".
During the 1980s, a battle for control of the store formed part of a long-running feud between Mr Al Fayed and the late businessman Tiny Rowland.
Mr Rowland later accused his business rival of breaking into a safety deposit box stored at Harrods.
Mr Al Fayed waged a 10-year campaign in an attempt to prove that Princess Diana and his son Dodi, who died in a Paris car crash in 1997, were murdered in a conspiracy.
Despite living in Britain for decades, the multi-millionaire businessman has repeatedly been refused a UK passport.
sigh how very depressing is all this?
Rumpelstiltskinsky 1 year ago
@MrSmasher1985 Yes I am homeless if you don't count my house, my apartment in London and my retreat in the Lake District. Of course you hate English people. We have developed a system where those born in humble circumstances can better themselves and earn huge amounts of money not available to simple minded bigots like you.
spiderofgod 1 year ago
@MrSmasher1985 banned for abuse. don't come back.
BritainDivided 1 year ago
@spiderofgod _!_ horrible place and you cant go there cuz u r homeless and you get paid from your asshole how much i hate fuckin English people ,they are scum on earth
MrSmasher1985 1 year ago
Hope the new owners have got better taste than Fayed. He made it look like a cheap film set. Horrible place.
spiderofgod 1 year ago