The baby, whose name was not yet announced, was born at 4:24 p.m. GMT and weighs 8 pounds 6 ounces.
The baby was born in the private Lindo Wing of St. Mary's Hospital, where Princess Diana gave birth to Prince William in 1982 and his younger brother, Prince Harry. William was present for the birth, officials said.
"Her Royal Highness and her child are both doing well and will remain in hospital overnight," the palace said in a statement.
The child is third in line to the British throne after Prince Charles and William.
"Both my wife and I are overjoyed at the arrival of my first grandchild. It is an incredibly special moment for William and Catherine and we are so thrilled for them on the birth of their baby boy," Prince Charles said in a statement. "Grandparenthood is a unique moment in anyone's life, as countless kind people have told me in recent months, so I am enormously proud and happy to be a grandfather for the first time and we are eagerly looking forward to seeing the baby in the near future."
The baby's birth certificate was driven from the hospital to Buckingham Palace, where it was placed on an easel for everyone to see. The baby's official new title is Royal Highness, Prince (name) of Cambridge.
There's so much excitement about the royal baby that U.K. retailers are anticipating an avalanche of baby-related merchandise sales. Some estimates put it at $400 million in souvenirs and festivities.
Palace officials confirmed Kate was admitted to the hospital in the early stages of labor around 6 a.m. GMT Monday. William and Kate traveled by car from Kensington Palace to St. Mary's Hospital, where they entered through a side door and dodged the world's media. About 90 minutes later, palace officials confirmed her arrival in a statement.
Throughout the birthing process, the 31-year-old has been looked after by a top-notch medical team led by royal gynecologist Dr. Marcus Setchell and assisted by Alan Farthin.
Royal officials were forced to announce the pregnancy in December after the Duchess' admission into the hospital for hyperemesis gravidarum, a serious condition that causes severe vomiting and dehydration.
William and Kate married in 2011 after a long courtship.
The Associated Press and ABC News contributed to this report.