William's late mother, Princess Diana, strived for a normal life for the prince and his brother, Prince Harry.
The move will also mean Charlotte and Louis will switch from their prep school in Battersea, south London, to one nearer by next month.
The royal couple had made Kensington Palace their main home since 2017, while they also have Anmer Hall in the Norfolk countryside, a stone's throw away from the monarch's Sandringham Estate, where the British royals traditionally celebrate Christmas.
A source also told the Sun of the move to Adelaide Cottage: "[Catherine] and William were very keen for a modest home to start their new lives in Windsor.
"Adelaide Cottage fits the bill because it is a four-bedroom home and they do not need any more as they have no live-in staff.
"They had no other demands than a pleasant family home close to schools and the Queen."
Although Adelaide will become their main home, they will still have their Kensington Palace apartment.