The legal warning came in response to an incident in which the photographer allegedly followed Prince George and his nanny, Maria Borrallo, to Battersea Park in south-west London.
He then attempted to take pictures of them, but was chased off.
According to the letter, the incident caused Prince William and the Duchess to strongly suspect that the freelancer concerned had been monitoring one-year-old George's movements, effectively placing him under surveillance.
A Clarence House spokesperson confirmed that the official warning had been issued and clarified the Duke and Duchess' position on press and privacy.
"The Duke and Duchess have taken legal steps to ask that an individual ceases harassing and following both Prince George and his nanny as they go about their ordinary daily lives."
The official statement went on to say that the Duke and Duchess 'understand the particular public role that Prince George will one day inherit' but believe that he is entitled to live as ordinary a childhood as possible.
"No parent would tolerate the suspicion of someone pursuing and harassing their child and carer whilst their child is playing in a public park or going about their daily activities," it added.
Prince William is said to be growing increasingly frustrated with what he sees as an unreasonable level of press intrusion into the everyday lives of his family.
Legal action was previously taken in 2012 against French tabloid magazine Closer after they published photos of a topless Kate sunbathing, obtained without her knowledge or consent using long lens photography.
French courts ruled in favour of the former Kate Middleton, and ordered Closer to hand over all the photos and remove them from their website within 24 hours or face a penalty of €10,000 per day.
A statement issued by St James Palace at the time emphasised the particularly personal upset that such intrusion caused the Prince.
"The incident is reminiscent of the worst excesses of the press and paparazzi during the life of Diana, Princess of Wales, and all the more upsetting to The Duke and Duchess for being so."