Sources claim that Mr Clarkson was encouraged to draw up the apology after penning a newspaper column in which he said he hoped that the Duchess of Sussex would one day be forced to parade naked through the streets of Britain, while a crowd chanted “shame” and threw “excrement” at her.
The TV personality previously claimed that he had “clumsily” referenced a scene in Game of Thrones in devising the controversial tableau.
The column fell foul to vehement online criticism, with the press watchdog Ipso receiving more than 20,000 complaints to become their most complained-about article ever.
The Mail on Sunday now reports that a mutual friend persuaded the former Top Gear host to write to the prince after some pubs refused to stock his beer, Hawkstone, in the wake of his comments about Meghan.
It claims that Mr Clarkson's business partner Johnny Hornby, who is also on the board of Prince Harry's charity Sentebale, had been the architect of the apology.
The newspaper understands that Mr Hornby, co-founder of Hawkstone along with Clarkson, feared that more pubs would drop the lager.
A source said: “Johnny is friends with both Jeremy and Harry so he was kind of in the middle of it all. He suggested that it would be a good idea for Jeremy to apologise. It was, after all, at a time when the beer's reputation was being affected.
“Jeremy decided he would do it and everyone now hopes that they can move on from it.”
Hawkstone lager, made using ingredients grown at Clarkson's Diddly Squat Farm in the Cotswolds, is sold in pubs across London, Buckinghamshire, Kent and Worcestershire.
Landlord Tom Doggett, of the Red Lion pub in Evesham, Worcestershire, told the Mail on Sunday he had removed the lager from his establishment because he says he wanted to “stick to his principles:
Explaining his decision to ban the lager, he said: “We have a lot of women who come here on their own and they say they feel safe in the pub. And if someone in the pub made comments like Jeremy Clarkson, at the very least I would ask them to be quiet or kick them out.”
The Independent has approached Mr Clarkson for comment.