Court documents show that the newspaper, and its sister website MailOnline, invaded the Duchess of Sussex’s privacy.
The news outlet has conceded defeat in a long-running court battle after it published a private letter Meghan sent to her father.
In a separate matter, an unspecified amount of money will also be paid to the Duchess for infringing on her copyright by publishing large parts of the letter.
The Guardian reports media lawyer Mark Stephens, who is not connected to the case, saying the £1 may show there was a weakness in the privacy aspect of Meghan’s case.
“Normally for that kind of invasion of privacy you would expect £75,000 to £125,000,” he said.
“It does show that the curation of her reputation was an area where she had effectively invaded her own privacy.”
The Mail on Sunday will also pay a large part of Markle’s legal fees, which could total more than £1 million.
A statement from Meghan’s legal team said any payouts will be donated to charity.
As part of the court’s order, The Mail on Sunday made a statement which was posted at the bottom of its front-page and on MailOnline on December 26.
"The Duchess of Sussex wins her legal case for copyright infringement against Associated Newspapers for articles published in The Mail on Sunday and posted on Mail Online,” it said.
The tabloid added “financial remedies have been agreed" but provided no extra details.
As part of a series of stories in 2019, The Mail On Sunday published large excerpts of the personal letter between Meghan and her father, Thomas Markle.