The 34-year-old duke of Sussex spoke to reporters Monday after Markle, duchess of Sussex, gave birth to a baby boy.
"Mother and baby are doing incredibly well," Harry said, according to Sky News. "It's been the most amazing experience I could ever possibly imagine."
"How any woman does what they do is beyond comprehension," he added. "But we're both absolutely thrilled and so grateful for all the love and support from everybody out there."
Harry said he and Markle are "still thinking" about a name for their son. The couple plan to announce the name and introduce their baby boy to the world "in probably two days time."
Harry said it was an "amazing" experience to witness the duchess give birth.
"As I said, I'm so incredibly proud of my wife," he said. "As every father and parent would ever say, your baby's absolutely amazing. This little thing is absolutely to die for so I'm just over the moon."
Harry and Markle had announced their son's birth in a post on their official Instagram account Monday.
"We are pleased to announce that Their Royal Highnesses The Duke and Duchess of Sussex welcomed their firstborn child in the early morning on May 6th, 2019. Their Royal Highnesses' son weighs 7lbs. 3 oz," the palace said.
"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," the palace added. "More details will be shared in the forthcoming days."
Markle went into labor early Monday morning with Harry by her side. The new baby is Queen Elizabeth II's eighth great-grandchild and seventh in line to the throne. The child shares a birthday with psychoanalyst Sigmund Freud, director Orson Welles, actor George Clooney and former British prime minister Tony Blair.
Harry and Markle married in May 2018 and announced Markle's pregnancy in October.
"Their Royal Highnesses have appreciated all of the support they have received from people around the world since their wedding in May and are delighted to be able to share this happy news with the public," the royal family said on Twitter at the time.
Harry and Markle established a separate court from Harry's brother, Prince William, and his wife, Kate Middleton, ahead of their baby boy's birth. The couple moved from Kensington Palace to Frogmore Cottage on the Windsor grounds.
"This long-planned move will ensure that permanent support arrangements for The Duke and Duchess's work are in place as they start their family," the palace said.
"Not only did many of you lend your support, you took action," the palace said. "YOU chose to be part of the collective good, and you have made a real difference."