The final straw reportedly came last week when one of the freelance photographers tried to take pictures of the young prince in Battersea Park with nanny Maria Teresa Turrion Borrallo.
Sources say there have also been a number of "clear privacy breaches" involving Prince George in recent weeks near his home at Kensington Palace.
According to the Daily Telegraph, a Kensington Palace spokesman said: "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.
"An incident last week has prompted Their Royal Highnesses to seek reasonable assurances from the individual about his behaviour. The individual was spotted at a central London Park in the vicinity of Prince George, who was removed from the Park immediately.
"There is reason to suspect that the individual may have been placing Prince George under surveillance and monitoring his daily routines for a period of time.
"The Duke and Duchess understand the particular public role that Prince George will one day inherit but while he is young, he must be permitted to lead as ordinary a life 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."
And a source told the Evening Standard: "Just like any parent, the Duke and Duchess want Prince George to have the freedom to safely experience normal childhood activities, like going to the park and playing with other children, without the threat of harassment or being placed under surveillance.
"One of the individuals has already been spoken to by protection officers about his behaviour in respect of members of the Royal Family on previous occasions over a number of years."
Kate herself has recently been out of the public eye while she recovers from acute morning sickness. She has been resting ever since it was revealed she is expecting her second child with Prince William.
Missing the Duchess' impeccable style? Don't worry, you can flick through our style gallery jam-packed with Kate M fashion pics: