In his book "Spare", Harry also discloses how the brothers, the sons of King Charles, had begged their father not to marry his second wife, Camilla, now Queen Consort, and that he had taken cocaine as a teenager.
The book was due to be published on Jan. 10, but the Guardian newspaper printed leaked extracts overnight, and Reuters and other media have been able to obtain Spanish-language versions which went on sale early in Spain.
Details of its contents come as ITV released a clip of an upcoming interview with Harry in which he said he could not commit to attending his father's coronation in May and defended his decision to speak out.
Harry's memoir gives a personal account of his struggles dealing with the death of his mother, Princess Diana, his time in the military - when he said he killed 25 Taliban insurgents while serving in Afghanistan - and his conflicts with the press.
But the most striking revelations concern the relationship with his family, something which has hung like a shadow over the British royals since he and Meghan stepped down from official duties in 2020 to move to California to forge a new life.
As is usual for the royal family, spokespeople for King Charles and Prince William have declined to comment.
Harry, 38, wrote in his memoir that his brawl with William, 40, took place in 2019 at his then London home after his brother had called Meghan "difficult", "rude" and "abrasive."
"He grabbed me by the collar, ripping my necklace, and he knocked me to the floor," Harry wrote.
"I landed on the dog's bowl, which cracked under my back, the pieces cutting into me. I lay there for a moment, dazed, then got to my feet and told him to get out."
William then challenged his younger brother to hit back, but Harry refused. William later returned to the scene, "looking regretful, and apologised", Harry wrote, with his brother asking him not to tell Meghan that he had "attacked" him.
William and Harry were once seen as very close after the death of their mother in a Paris car crash in 1997. But the brothers have fallen out since Harry married Meghan, a former actress, in 2018, and the couple then quit their royal role.
In another section of the book, Harry refers to his first meeting with Camilla, whom Diana had blamed for the break-up of her marriage. Harry says he and William had approved of Camilla, but asked their father not to marry her.
"Despite the fact that Willy and I asked him not to do it, my father went ahead," Harry wrote. "Despite the bitterness and sadness we felt in closing another loop in the history of our mother, we understood this was irrelevant."
Since their exit from royal life, the Duke and Duchess of Sussex, as Harry and Meghan are officially known, have delivered stinging criticism of the Windsors and the British monarchy which has included accusations of racism, which William has dismissed.
In an interview for the CBS show "60 Minutes," Harry said he himself was "probably bigoted before the relationship with Meghan."
"Put it this way, I didn't see what I now see," Harry added.
Last month their six-part Netflix documentary, which attracted record audiences, aired with renewed accusations, including that William had screamed at Harry during a crisis summit to discuss his future.
The main criticism from Harry and Meghan is that royal aides not only refused to hit back at hostile, inaccurate press coverage, but were complicit in leaking negative stories to protect other royals, most notably William.
"I don't know how staying silent is ever going to make things better," Harry said in Thursday's ITV clip.
Asked why he was invading the privacy of his family, something he had railed against, he replied: "That will be the accusation from the people that don't understand or don't want to believe that my family have been briefing the press."
The title of his book "Spare" comes from an oft-cited quote in British aristocratic circles about the need for an heir, and a spare.
Harry says Charles reputedly said to Diana on the day he was born: "Wonderful! Now you've given me an heir and a spare – my work is done."
How much the disclosures will resonate with the public is unclear. A YouGov poll this week found that 65% of those surveyed were "not interested at all" in his upcoming book, while another found greater sympathy among respondents for William and his wife, Kate, than for Harry and Meghan.
Charles himself is still hoping for a reconciliation with his son, unnamed sources told newspapers this week.
In its leaked extracts, the Guardian says the king had stood between his two sons during a difficult meeting at Windsor Castle following the April 2021 funeral for their grandfather Prince Philip, the late Queen Elizabeth's husband.
"Please, boys," Harry quoted his father as saying, "don’t make my final years a misery."