The new dad spoke to cameras outside of Windsor Castle to say that mom and baby were both "doing incredibly well."
"I'm very excited to announce that Meghan and myself had a baby boy early this morning, a very healthy boy," Harry said through a big grin. "Mother and baby are doing incredibly well. It's been the most amazing experience I could ever possibly imagine. How any woman does what they do is beyond comprehension but we're both absolutely thrilled and so grateful to all the lovely support."
When asked if they would announce a name for their child, Harry said they are "still thinking about names."
"The baby is a little bit overdue so we've had a little bit of time to think about it. That's the next bit," he teased confirming he and Meghan will make their debut as a family in two days "as planned."
"I haven't been to many births. This is definitely my first birth. It was amazing, absolutely incredible," Harry continued. "And as I said, I'm so incredibly proud of my wife and as every father and parent would ever say you know your baby is absolutely amazing. But this little thing is, is absolutely to die for.
"So, I'm just over the moon."
The couple announced via Instagram Monday that their firstborn child weighed in at 7-pounds 3-ounces. The baby, who has not yet been named, is seventh in line for the British throne and is Queen Elizabeth II's eighth great-grandchild. Harry is the younger son of Prince Charles, the next in line to the throne, and the late Princess Diana.
Markle, 37, and 34-year-old Prince Harry did not disclose the location they chose for the birth and throughout Meghan's pregnancy, they never revealed the baby's due date. They have said they didn't find out the sex in advance.
Their child is eligible for dual British-U.S. citizenship if Meghan wants to go through the application process.
Officials say senior royals including Queen Elizabeth II have been informed of the birth, as has the family of his late mother, Princess Diana.
Harry and Meghan married at Windsor Castle a year ago this month. In April, they moved 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.
The Associated Press contributed to this report.