Thomas's Battersea is a preparatory school located a few miles from the family residence in Kensington Palace.
The duke and duchess said they were "delighted" to have found a school for their son - the third in line to the throne - who turns four in July.
The school's headmaster, Ben Thomas, said he was "honoured" to welcome the prince as a pupil.
He said: "We greatly look forward to welcoming him and all of our new pupils to the school in September."
Prince William and Catherine, Duchess of Cambridge, said "they are confident George will have a happy and successful start to his education".
Prince George, who is third in line to the throne after his grandfather Prince Charles and his father, currently goes to a nursery in Norfolk, Westacre Montessori School.
Thomas's Battersea charges more than Â£6,000 a term, according to the 2017 Tatler Schools Guide.
The royal couple recently announced plans to move from their main home in Norfolk, Anmer Hall, to their apartment in Kensington Palace as Prince William takes on more royal duties.
Princess Charlotte, who turns two in May, will start nursery in the summer.
By Peter Hunt, BBC royal correspondent
When it comes to education, the royals have embraced change, but not revolutionary change.
Prince George's great-grandmother had a governess.  A home based education was the norm for upper class girls like the future Queen.
While the third in line to the throne prepares to join more than 500 other pupils, his grandfather, at around the same age, was having a blackboard and a desk installed in a room at Buckingham Palace.
A week before his eighth birthday, in a break with royal convention, Prince Charles did go to school.
His peer group was then able to use the palace swimming pool because it was thought inappropriate for the heir to the throne to use a public one.
George will probably be spared what was inflicted on princes William and Harry on their first day at school. Photographers and camera crews are unlikely to be invited to record the moment.
It will be the start of the prince's private education. The prospect of a state educated British king or queen remains a remote one.
Read more from Peter
The Duke and Duchess of Cambridge will send Prince George to a private south London primary school in September.