He said the first official photos of the newest royal will be released Wednesday, at which time his name is also expected to be revealed.
Following royal tradition, a notice of the boy’s birth was displayed Monday outside Buckingham Palace.
The 37-year-old Duchess of Sussex, who was an American actress known as Meghan Markle before she joined the British royal family, went into labor in the early hours Monday, officials said in a statement obtained by ITV News.
“The Duke of Sussex was by Her Royal Highnesses’ side,” palace officials said in the announcement.
Throughout Meghan's pregnancy, the couple never revealed the due date and said they decided not to find out the baby's sex in advance.
They announced they were expecting their first child in October, five months after they wed in a star-studded ceremony at England’s Windsor Castle.
The child will be the seventh in line for the throne. He or she will also be eligible for dual British-U.S. citizenship.
Harry and Meghan moved in April from a house on the London grounds of Kensington Palace to Frogmore Cottage, which is on the property near Windsor Castle where they held their wedding reception.
Kensington Palace officials have said the new parents don't plan to pose for a photograph or appear in public with their baby for several days after the birth.
The Associated Press contributed to this report.
Check back for updates to this developing story.