Prince Harry said the new parents were "absolutely thrilled" and thanked the public for their support during the pregnancy: "It's been the most wonderful experience I could ever have possibly imagined".
Grinning from ear to ear, the Duke of Sussex said Meghan gave birth to a baby boy early Monday morning (Monday afternoon, New Zealand time).
The baby's sex will be a surprise for the couple, who chose not to find out what they were having.
Conservative Leader Andrew Scheer also sent best wishes to the new parents, wishing them "all the best on the birth of their baby boy".
In a statement the Palace said that the Queen, the Duke of Edinburgh, the Prince of Wales, the Duchess of Cornwall and the Duke and Duchess of Cambridge were all "delighted" with the news. "This little thing is absolutely to die for so I'm just over the moon".
Meghan Markle's own father's name, Thomas, even made the betting lists despite their frayed relationship.
The as-yet-unnamed baby arrived less than a year after Prince Harry Wednesday Meghan Markle in a spectacular televised event on the grounds of Windsor Castle that was watched the world over.
The new royal baby is seventh in line for the throne.
It is the first child for Harry and Meghan, who married a year ago. We are both thrilled, grateful to all the support. In 1917, revolutions were threatening to take down royal families across Europe.
Shortly after Meghan's pregnancy was announced, Kate shared her excitement about the news while chatting with the crowd gathered during a November visit to Leicester University. 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.