Harry and Meghan claimed the footage was an invasion of privacy and launched a lawsuit in Los Angeles in July.
In their trial, the couple said an individual photographed Archie, then 14 months old, at their home during the coronavirus confinement.
Their lawyer Michael Kump said on Thursday that the responsible agency, X17, apologized and agreed to a “reimbursement of legal fees.”
He added: “Over the summer, the Duke and Duchess of Sussex took action against intrusive and illegal paparazzi photos taken of their family at a private residence.
“Today, the agency responsible for these photos – X17 – apologized and accepted a permanent injunction and reimbursement of legal fees.
“It’s a positive result. All families have the right, protected by law, to feel safe at home. ”
The photos in question were of Archie and Meghan’s mother Doria Ragland, according to Los Angeles County Superior Court documents.
X17 agreed to hand over the photos to Harry and Meghan and destroy all copies of its archives or databases.
She also pledged never again to tamper with the photos of the couple or their son taken by drone, zoom or telephoto lens “in any private residence or on the surrounding private land”.
Harry and Meghan claimed in their lawsuit that they had lived “safely” in North Saanich, Canada, for six weeks before the media published their new location.
They said the published photos had prompted “up to 40 paparazzi and media organizations to descend upon this peaceful community hundreds of miles away.”
The couple claimed drones flew 20 feet above their home as often as three times a day and that photos of Archie were sold.
Helicopters also flew over the residence from 5:30 am and until 7:00 pm, which, according to legal papers, had the effect of “waking the neighbors and their son, day after day”.
Photographers allegedly drilled holes in the security fence, the lawsuit said.
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The lawsuit says the former royal couple want to do what is “necessary to protect their children from this manufactured binge eating.”
Harry and Meghan, who announced their resignation as royals in March, say they are “not asking for any special treatment” and just want the right to privacy.
Meghan is also suing Associated Newspapers – publisher of The Mail on Sunday and MailOnline – over articles which published parts of a “private and confidential” letter from the Duchess to her former father, Thomas Markle.