Before Markle gave birth, a palace statement said that they would be celebrating the occasion privately before making press appearances.
"Their Royal Highnesses have taken a personal decision to keep the plans around the arrival of their baby private," the statement said. "The Duke and Duchess look forward to sharing the exciting news with everyone once they have had an opportunity to celebrate privately as a new family."
Speaking to reporters after the baby was born, Harry said they would hold a photo call with the new baby in two days.
"That's the next bit, but for us, we will be seeing you guys in two days time as planned as a family to be able to share it with you guys, so everybody can see the baby," he said.