She was admitted to the private Lindo wing of St. Mary's Hospital Monday morning in the early stages of labor, a statement from Kensington Palace said.
Her husband Prince William, the Duke of Cambridge, is with her, the statement said.
They traveled to St. Mary's from Kensington Palace by car, not by ambulance. The west London hospital is where William himself was born in 1982.
The duchess is thought to be about one week past her due date, according to the BBC's royal correspondent, Peter Hunt.
Officials would not comment on whether her labor would have to be induced, he said.
Via Twitter, Hunt tweeted:
According to Kate's spokesman, " things are progressing as normal".
The royal baby will be third in line to the British throne, after his or her grandfather, Prince Charles, and father, Prince William.
The child's royal title will be the Prince or Princess of Cambridge, Buckingham Palace announced earlier this month.
Last week, the Queen joked about the imminent arrival of the newest member of her family, saying she hoped the baby was born before she went on holiday to her private Balmoral estate in Scotland.
During a visit to the National Railway Museum in York, the Prince of Wales was asked by the members of the press and the public about the birth of his first grandchild but he did not divulge any information.
Prince William has been with his wife on annual leave and will have two weeks' paternity leave from his job as an RAF search and rescue helicopter pilot.