Proud new father Harry, 34, gave a short TV interview after the announcement on Monday, saying he was ‘over the moon’ about his arrival.
He added: “We’ll be seeing you guys in probably two days time as planned, as a family, to be able to share it with you guys so everyone can see the baby.”
While the duke and duchess opted out of an initial post-birth photo call, it’s likely the world will get the first glimpse of their baby boy on Wednesday.
Royal commentator Omid Scobie tweeted: “It will be a quiet day in terms of announcements but tomorrow’s photo call is not far away.”
He added: “I’m told their first night as a family of three was peaceful and emotional.”
Originally it was believed that Meghan had a home birth, but reports have since emerged that she was taken to a London hospital - likely The Portland - on Sunday evening.
A ‘basic’ delivery costs upwards of £15,000 at the private maternity hospital.
Buckingham Palace has declined to comment, while a spokeswoman for The Portland told Yahoo UK: “We are unable to confirm speculation about individuals who may or may not have been cared for at The Portland Hospital."
The baby’s name is also yet to be announced. Harry said he and Meghan “are still thinking about names.”
James, Alexander and Arthur are among the frontrunners in the latest royal baby name odds, according to bookmakers.