"The baby is a little bit over due so we've had a little time to think about it (names)," he said.
"That's the next bit, but for us, we will seeing you guys in two days time, as planned as a family to be able to share with you guys, so everybody can see the baby."
The Duke of Sussex added: "It's absolutely incredible and I'm so incredibly proud of my wife."
Harry, who was present for the birth, said his son was "absolutely to die for … I'm absolutely over the moon".
The birth was announced, as expected, on the couple's new Instagram page. A formal announcement followed soon after.
"Her Royal Highness The Duchess of Sussex was safely delivered of a son at 0526hrs (2.26pm Monday AEST)," Buckingham Palace said in a statement. "The baby weighs 7lbs 3oz (3.26kg).
"The Duke of Sussex was present for the birth." It is
The statement continued: "The Duchess and baby are both healthy and well, and the couple thank members of the public for their shared excitement and support during this very special time in their lives.
More details will be shared in the forthcoming days," they posted on Instagram.
Meghan's mum Doria Ragland was by her side during the birth, having flown into the UK from Los Angeles late last month.
The home birth was a return to royal tradition — the Queen had all four of her children at home at Buckingham Palace.
Harry and Meghan made it clear in a statement last month they wanted to keep the details of the birth private and would not be taking part in the traditional photo call after the birth as Kate Middleton and Prince William have done with all three of their children.
