According to the palace, the baby will be known as His Royal Highness Prince George of Cambridge.
The queen's father is George the Sixth, and her grandfather is George the Fifth.
Earlier in the day, the baby met his great-grandmother, Queen Elizabeth II, Prince Harry and his aunt, Pippa Middleton. After the visit, the child was taken to see Kate's parents in their village near London.
ABC News has learned that Kate and William spent their first night out of the hospital without a nanny because they wanted to bond with their new son alone.
The baby was born Monday, weighing 8 pounds 6 ounces, at 4:24 p.m. London time. The official birth announcement didn't come until nearly four hours after the birth so that the couple could call family and friends to personally share their news.
Officials say William was with Kate throughout the entire birth and also stayed with her at the hospital overnight, which is rare for a royal.
On Tuesday, the new parents appeared outside St. Mary's Hospital to show the world Britain's future monarch. The Duke and Duchess of Cambridge brought their son out to the very same hospital steps where William himself made his debut 31 years ago. The family posed for photos and answered a few questions.
A smiling Kate, who wore a pale blue polka-dot dress, said she felt "very emotional." She passed the baby to her husband, who appeared relaxed and joked with reporters.
"He's got her looks, thankfully," William said. "He's got a good pair of lungs on him, that's for sure."
William added: "He's a big boy, he's quite heavy," and laughed when a reporter asked him about the baby's hair.
The couple will raise their bundle of joy in apartment 1A of Kensington Palace, which has more than 20 rooms. It's also the same palace in which William grew up, noted for its ornate interior décor and picturesque gardens.
In a statement, the new parents said, "We would like to thank the staff at the Lindo Wing and the whole hospital for the tremendous care the three of us have received. We know it has been a very busy period for the hospital and we would like to thank everyone - staff, patients and visitors - for their understanding during this time."
The Associated Press and ABC News contributed to this report.