As he stood in front of the stables unable to conceal his joy, the duke said he was "very excited" to announce the birth of the couple's newborn son.
"I’m very excited to announced that Meghan. and myself had a baby boy early this morning, a very healthy boy," he said.
The royal went on to express his admiration for women's strength in the act of childbirth.
"How any woman does what they do is beyond comprehension," Prince Harry said.
"We're both absolutely thrilled and so grateful for all the love and support from everybody out there. It's been amazing."
Prince Harry stated that both Meghan and their baby, whose name is yet to be revealed, are both doing "incredibly well".
Ian Lloyd, a royal photographer and commentator, said that new father's expression of emotion is "typical of him".
"He is expressing the sheer wonder of childbirth and how you feel at this awesome moment in your life," Lloyd tells The Independent.
"It's typical of him as he is able to express those emotions. Traditionally, the royal family would never have said that."
Lloyd adds that the nature of Prince Harry's announcement is a sign of how he and Meghan "function as a couple".
"It's a move away from the traditional royal reticence of expressing emotions. He is a new-age father," the photographer states.
Several royal fans have praised Prince Harry for his appreciation of the difficulties of childbirth.
"The kudos he gave to his wife, and all women for going through the process of childbirth was beautiful!!" one person tweeted.
"Listening to Prince Harry talk about the birth of his son (and tearing up) and praise women for the powerful work of #childbirth gave me all the feels this morning," another remarked.
"I can't help but tear up myself and think 'his mother would be so proud of the man he is'."
For all the latest news on the birth of the royal baby, follow The Independent's live blog here.